what is the solution to this system of linear equations brainly

Graphs

33 Graph Linear Equations in 2 Variables

Learning Objectives

Past the end of this section, you volition be able to:

Recognize the relationship between the solutions of an equation and its graph.
Graph a linear equation by plotting points.
Graph vertical and horizontal lines.

Recognize the Relationship Betwixt the Solutions of an Equation and its Graph

In the previous section, nosotros found several solutions to the equation $3x+2y=6$ . They are listed in (Figure). Then, the ordered pairs $\left(0,3\right)$ , $\left(2,0\right)$ , and $\left(1,\frac{3}{2}\right)$ are some solutions to the equation $3x+2y=6$ . We can plot these solutions in the rectangular coordinate organization every bit shown in (Figure).

$3x+2y=6$
$x$	$y$	$\left(x,y\right)$
0	3	$\left(0,3\right)$
2	0	$\left(2,0\right)$
1	$\frac{3}{2}$	$\left(1,\frac{3}{2}\right)$

The figure shows four points on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the four points at (0, 3), (1, three halves), (2, 0), and (4, negative 3). The four points appear to line up along a straight line.

Observe how the points line upwards perfectly? We connect the points with a line to get the graph of the equation $3x+2y=6$ . See (Figure). Detect the arrows on the ends of each side of the line. These arrows indicate the line continues.

Every signal on the line is a solution of the equation. Too, every solution of this equation is a signal on this line. Points non on the line are not solutions.

Notice that the point whose coordinates are $\left(-2,6\right)$ is on the line shown in (Figure). If yous substitute $x=-2$ and $y=6$ into the equation, you find that it is a solution to the equation.

The figure shows a straight line and two points and on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. Dots mark off the two points and are labeled by the coordinates

The figure shows a series of equations to check if the ordered pair (negative 2, 6) is a solution to the equation 3x plus 2y equals 6. The first line states

So the indicate $\left(-2,6\right)$ is a solution to the equation $3x+2y=6$ . (The phrase "the signal whose coordinates are $\left(-2,6\right)$ " is oft shortened to "the point $\left(-2,6\right)$ .")

The figure shows a series of equations to check if the ordered pair (4, 1) is a solution to the equation 3x plus 2y equals 6. The first line states

So $\left(4,1\right)$ is non a solution to the equation $3x+2y=6$ . Therefore, the betoken $\left(4,1\right)$ is not on the line. See (Effigy). This is an example of the saying, "A moving-picture show is worth a thousand words." The line shows yous all the solutions to the equation. Every point on the line is a solution of the equation. And, every solution of this equation is on this line. This line is chosen the graph of the equation $3x+2y=6$ .

Graph of a Linear Equation

The graph of a linear equation $Ax+By=C$ is a line.

Every bespeak on the line is a solution of the equation.
Every solution of this equation is a point on this line.

The graph of $y=2x-3$ is shown.

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line has a positive slope and goes through the y-axis at the (0, negative 3). The line is labeled with the equation y equals 2x negative 3.

For each ordered pair, decide:

ⓐ Is the ordered pair a solution to the equation?
ⓑ Is the point on the line?

A $\left(0,-3\right)$ B $\left(3,3\right)$ C $\left(2,-3\right)$ D $\left(-1,-5\right)$

Employ the graph of $y=3x-1$ to decide whether each ordered pair is:

a solution to the equation.
on the line.

ⓐ $\left(0,-1\right)$ ⓑ $\left(2,5\right)$

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the point (negative 2, negative 7) and for every 3 units it goes up, it goes one unit to the right. The line is labeled with the equation y equals 3x minus 1.

ⓐ yes, ayeⓑ yes, yes

Use graph of $y=3x-1$ to make up one's mind whether each ordered pair is:

a solution to the equation
on the line

ⓐ $\left(3,-1\right)$ ⓑ $\left(-1,-4\right)$

ⓐ no, noⓑ yes, yes

Graph a Linear Equation by Plotting Points

There are several methods that can be used to graph a linear equation. The method we used to graph $3x+2y=6$ is called plotting points, or the Indicate–Plotting Method.

How To Graph an Equation Past Plotting Points

Graph the equation $y=2x+1$ by plotting points.

Graph the equation by plotting points: $y=2x-3$ .

Graph the equation by plotting points: $y=-2x+4$ .

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), (4, negative 4), and (5, negative 6). There are arrows at the ends of the line pointing to the outside of the figure.

The steps to accept when graphing a linear equation by plotting points are summarized below.

Graph a linear equation past plotting points.

Discover 3 points whose coordinates are solutions to the equation. Organize them in a tabular array.
Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, advisedly cheque your work.
Describe the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

It is true that it simply takes 2 points to make up one's mind a line, only it is a practiced habit to use three points. If you only plot two points and one of them is incorrect, you tin can still draw a line but it volition not represent the solutions to the equation. It will exist the wrong line.

If you use 3 points, and one is incorrect, the points will not line up. This tells you something is incorrect and you need to cheque your work. Look at the difference between part (a) and role (b) in (Figure).

Figure a shows three points with a straight line going through them. Figure b shows three points that do not lie on the same line.

Let's do another case. This time, nosotros'll show the concluding 2 steps all on 1 filigree.

Graph the equation $y=-3x$ .

Solution

Observe 3 points that are solutions to the equation. Here, again, it'due south easier to choose values for $x$ . Do you see why?

We list the points in (Effigy).

$y=-3x$
$x$	$y$	$\left(x,y\right)$
0	0	$\left(0,0\right)$
1	$-3$	$\left(1,-3\right)$
$-2$	6	$\left(-2,6\right)$

Plot the points, check that they line upward, and draw the line.

Graph the equation by plotting points: $y=-4x$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 8), (0, 0), and (2, negative 8). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation by plotting points: $y=x$ .

When an equation includes a fraction as the coefficient of $x$ , we tin can notwithstanding substitute any numbers for $x$ . Simply the math is easier if nosotros make 'good' choices for the values of $x$ . This way we will avert fraction answers, which are hard to graph precisely.

Graph the equation $y=\frac{1}{2}x+3$ .

Graph the equation $y=\frac{1}{3}x-1$ .

Graph the equation $y=\frac{1}{4}x+2$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 12, negative 1), (negative 8, 0), (negative 4, 1), (0, 2), (4, 3), (8, 4), and (12, 5). The line has arrows on both ends pointing to the outside of the figure.

Then far, all the equations nosotros graphed had $y$ given in terms of $x$ . Now we'll graph an equation with $x$ and $y$ on the same side. Let's run into what happens in the equation $2x+y=3$ . If $y=0$ what is the value of $x$ ?

This indicate has a fraction for the x– coordinate and, while we could graph this point, it is difficult to be precise graphing fractions. Remember in the instance $y=\frac{1}{2}x+3$ , we carefully chose values for $x$ then as non to graph fractions at all. If we solve the equation $2x+y=3$ for $y$ , information technology will exist easier to observe three solutions to the equation.

$\begin{array}{ccc}\hfill 2x+y& =\hfill & 3\hfill \\ \hfill y& =\hfill & -2x+3\hfill \end{array}$

The solutions for $x=0$ , $x=1$ , and $x=-1$ are shown in the (Effigy). The graph is shown in (Figure).

$2x+y=3$
$x$	$y$	$\left(x,y\right)$
0	3	$\left(0,3\right)$
one	ane	$\left(1,1\right)$
$-1$	5	$\left(-1,5\right)$

Can yous locate the signal $\left(\frac{3}{2},0\right)$ , which we constitute past letting $y=0$ , on the line?

Graph the equation $3x+y=-1$ .

Graph the equation $2x+y=2$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 2, 6), (0, 2), (2, negative 2), (4, negative 6), and (6, negative 10). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $4x+y=-3$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 9), (negative 2, 5), (negative 1, 1), (0, negative 3), (1, negative 7), and (2, negative 10). The line has arrows on both ends pointing to the outside of the figure.

If you can cull any iii points to graph a line, how will y'all know if your graph matches the one shown in the answers in the volume? If the points where the graphs cross the x– and y-axis are the same, the graphs match!

The equation in (Figure) was written in standard grade, with both $x$ and $y$ on the same side. Nosotros solved that equation for $y$ in only one step. Simply for other equations in standard grade it is not that easy to solve for $y$ , so we will go out them in standard course. We can still find a first point to plot by letting $x=0$ and solving for $y$ . We tin can plot a second point past letting $y=0$ and and then solving for $x$ . Then we will plot a tertiary betoken by using some other value for $x$ or $y$ .

Graph the equation $2x-3y=6$ .

Graph the equation $4x+2y=8$ .

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $2x-4y=8$ .

Graph Vertical and Horizontal Lines

Can we graph an equation with only 1 variable? Just $x$ and no $y$ , or merely $y$ without an $x$ ? How will we brand a table of values to get the points to plot?

Allow's consider the equation $x=-3$ . This equation has only one variable, $x$ . The equation says that $x$ is always equal to $-3$ , so its value does not depend on $y$ . No thing what $y$ is, the value of $x$ is ever $-3$ .

So to make a table of values, write $-3$ in for all the $x$ values. Then choose any values for $y$ . Since $x$ does not depend on $y$ , you lot can choose any numbers you like. But to fit the points on our coordinate graph, we'll apply i, ii, and 3 for the y-coordinates. See (Figure).

$x=-3$
$x$	$y$	$\left(x,y\right)$
$-3$	1	$\left(-3,1\right)$
$-3$	2	$\left(-3,2\right)$
$-3$	3	$\left(-3,3\right)$

Plot the points from (Figure) and connect them with a straight line. Notice in (Figure) that we have graphed a vertical line.

Vertical Line

A vertical line is the graph of an equation of the form $x=a$ .

The line passes through the x-axis at $\left(a,0\right)$ .

Graph the equation $x=2$ .

Graph the equation $x=5$ .

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.

Graph the equation $x=-2$ .

What if the equation has $y$ only no $x$ ? Let's graph the equation $y=4$ . This time the y– value is a constant, so in this equation, $y$ does not depend on $x$ . Fill in 4 for all the $y$ 'due south in (Figure) and and so cull whatsoever values for $x$ . We'll use 0, ii, and four for the x-coordinates.

$y=4$
$x$	$y$	$\left(x,y\right)$
0	4	$\left(0,4\right)$
two	iv	$\left(2,4\right)$
4	4	$\left(4,4\right)$

The graph is a horizontal line passing through the y-axis at 4. Run across (Figure).

Horizontal Line

A horizontal line is the graph of an equation of the form $y=b$ .

The line passes through the y-axis at $\left(0,b\right)$ .

Graph the equation $y=-1.$

Graph the equation $y=-4$ .

Graph the equation $y=3$ .

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 3), (0, 3), (4, 3), and all other points with second coordinate 3. The line has arrows on both ends pointing to the outside of the figure.

The equations for vertical and horizontal lines look very similar to equations like $y=4x.$ What is the difference between the equations $y=4x$ and $y=4$ ?

The equation $y=4x$ has both $x$ and $y$ . The value of $y$ depends on the value of $x$ . The y-coordinate changes according to the value of $x$ . The equation $y=4$ has but one variable. The value of $y$ is constant. The y-coordinate is e'er 4. It does not depend on the value of $x$ . See (Figure).

$y=4x$			$y=4$
$x$	$y$	$\left(x,y\right)$	$x$	$y$	$\left(x,y\right)$
0	0	$\left(0,0\right)$	0	4	$\left(0,4\right)$
one	4	$\left(1,4\right)$	1	4	$\left(1,4\right)$
2	8	$\left(2,8\right)$	2	iv	$\left(2,4\right)$

The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. One line is a straight horizontal line labeled with the equation y equals 4. The other line is a slanted line labeled with the equation y equals 4x.

Observe, in (Figure), the equation $y=4x$ gives a slanted line, while $y=4$ gives a horizontal line.

Graph $y=-3x$ and $y=-3$ in the same rectangular coordinate arrangement.

Graph $y=-4x$ and $y=-4$ in the same rectangular coordinate arrangement.

Graph $y=3$ and $y=3x$ in the same rectangular coordinate system.

Key Concepts

Graph a Linear Equation by Plotting Points
1. Discover 3 points whose coordinates are solutions to the equation. Organize them in a tabular array.
2. Plot the points in a rectangular coordinate system. Cheque that the points line upward. If they practice not, advisedly bank check your work!
3. Draw the line through the three points. Extend the line to make full the grid and put arrows on both ends of the line.

Practice Makes Perfect

Recognize the Human relationship Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, determine:

ⓐ Is the ordered pair a solution to the equation?ⓑ Is the point on the line?

ⓐ yes; noⓑ no; noⓒ yep; yesⓓ yes; yes

ⓐ yes; yepⓑ yes; yepⓒ yes; yeahⓓ no; no

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

$y=3x-1$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), and (3, 8).

$y=2x+3$

$y=-2x+2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, 10), (negative 3, 8), (negative 2, 6), (negative 1, 4), (0, 2), (1, 0), (2, negative 2), (3, negative 4), (4, negative 6), and (5, negative 8).

$y=-3x+1$

$y=x+2$

$y=x-3$

$y=\text{−}x-3$

$y=\text{−}x-2$

$y=2x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 5, negative 10), (negative 4, negative 8), (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10).

$y=3x$

$y=-4x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, 12), (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), (2, negative 8), and (3, negative 12).

$y=-2x$

$y=\frac{1}{2}x+2$

$y=\frac{1}{3}x-1$

$y=\frac{4}{3}x-5$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 3, negative 9), (0, negative 5), (3, negative 1), (6, 3), and (9, 7).

$y=\frac{3}{2}x-3$

$y=-\frac{2}{5}x+1$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 10, 5), (negative 5, 3), (0, 1), (5, negative 1), and (10, negative 3).

$y=-\frac{4}{5}x-1$

$y=-\frac{3}{2}x+2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 6, 11), (negative 4, 8), (negative 2, 5), (0, 2), (2, negative 1), (4, negative 4), (6, negative 7), and (8, negative 10).

$y=-\frac{5}{3}x+4$

$x+y=6$

$x+y=4$

$x+y=-3$

$x+y=-2$

$x-y=2$

$x-y=1$

$x-y=-1$

$x-y=-3$

$3x+y=7$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.

$5x+y=6$

$2x+y=-3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, 7), (negative 4, 5), (negative 3, 3), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 5), and (2, negative 7).

$4x+y=-5$

$\frac{1}{3}x+y=2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).

$\frac{1}{2}x+y=3$

$\frac{2}{5}x-y=4$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 5, negative 2), (0, negative 4), and (5, negative 6).

$\frac{3}{4}x-y=6$

$2x+3y=12$

$4x+2y=12$

$3x-4y=12$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 4, negative 6), (0, negative 3), (4, 0), and (8, 3).

$2x-5y=10$

$x-6y=3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, negative three halves), (negative 3, negative 1), (0, negative one half), (3, 0), and (6, one half).

$x-4y=2$

$5x+2y=4$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 7), (0, 2), (2, negative 3), and (4, negative 8).

$3x+5y=5$

Graph Vertical and Horizontal Lines

In the following exercises, graph each equation.

$x=4$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (4, 0), (4, 1), (4, 2) and all points with first coordinate 4.

$x=3$

$x=-2$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (negative 2, 0), (negative 2, 1), (negative 2, 2) and all points with first coordinate negative 2.

$x=-5$

$y=3$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, 3), (1, 3), (2, 3) and all points with second coordinate 3.

$y=1$

$y=-5$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The horizontal line goes through the points (0, negative 5), (1, negative 5), (2, negative 5) and all points with second coordinate negative 5.

$y=-2$

$x=\frac{7}{3}$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The vertical line goes through the points (7/3, 0), (7/3, 1), (7/3, 2) and all points with first coordinate 7/3.

$x=\frac{5}{4}$

$y=-\frac{15}{4}$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15/4), (1, negative 15/4), (2, negative 15/4) and all points with second coordinate negative 15/4.

$y=-\frac{5}{3}$

In the following exercises, graph each pair of equations in the same rectangular coordinate organization.

$y=5x$ and $y=5$

$y=-\frac{1}{3}x$ and $y=-\frac{1}{3}$

Mixed Practice

In the post-obit exercises, graph each equation.

$y=4x$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 8), (negative 1, negative 4), (0, 0), (1, 4), and (2, 8).

$y=2x$

$y=-\frac{1}{2}x+3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 6), (negative 4, 5), (negative 2, 4), (0, 3), (2, 2), (4, 1), and (6, 0).

$y=\frac{1}{4}x-2$

$y=\text{−}x$

$y=x$

$x-y=3$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 3, negative 7), (negative 2, negative 6), (negative 1, negative 4), (0, negative 3), (1, negative 2), (2, negative 1), (3, 0), (4, 1), (5, 2), and (6, 3).

$x+y=-5$

$4x+y=2$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, 6), (negative 1, 4), (0, 2), (1, negative 2), and (2, negative 6).

$2x+y=6$

$y=-1$

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 1), (1, negative 1), (2, negative 1) and all points with second coordinate negative 1.

$y=5$

$2x+6y=12$

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 6, 4), (negative 3, 3), (0, 2), (3, 1), and (6, 0).

$5x+2y=10$

$x=3$

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The vertical line goes through the points (3, 0), (3, 1), (3, 2) and all points with first coordinate 3.

$x=-4$

Everyday Math

Motor home cost. The Robinsons rented a motor home for i week to go along vacation. It toll them ?594 plus ?0.32 per mile to rent the motor home, so the linear equation $y=594+0.32x$ gives the price, $y$ , for driving $x$ miles. Summate the rental cost for driving 400, 800, and 1200 miles, and then graph the line.

?722, ?850, ?978

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.

Writing Exercises

Explain how y'all would choose three x– values to make a table to graph the line $y=\frac{1}{5}x-2$ .

Answers will vary.

What is the divergence between the equations of a vertical and a horizontal line?

Self Check

ⓐ Afterwards completing the exercises, use this checklist to evaluate your mastery of the objectives of this department.

This table has 4 rows and 4 columns. The first row is a header row and it labels each column. The first column header is

ⓑ Afterward reviewing this checklist, what will yous do to become confident for all goals?

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Source: https://opentextbc.ca/elementaryalgebraopenstax/chapter/graph-linear-equations-in-two-variables/

what is the solution to this system of linear equations brainly

33 Graph Linear Equations in 2 Variables

Learning Objectives

Recognize the Relationship Betwixt the Solutions of an Equation and its Graph

Graph a Linear Equation by Plotting Points

Graph Vertical and Horizontal Lines

Key Concepts

Practice Makes Perfect

Mixed Practice

Everyday Math

Writing Exercises

Self Check

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