Question

solve this system of equations by graphing. first graph the equations, and then type the solution.$2x - 3y = -18$$y = \frac{1}{3}x + 5$click to select points on the graph.the solution is $\left(\square, \square\
ight).$

Explanation:

Step1: Rewrite first equation to slope-intercept form

Rearrange $2x - 3y = -18$ to solve for $y$:
$-3y = -2x -18$
$y = \frac{2}{3}x + 6$

Step2: Identify points for first line

For $y = \frac{2}{3}x + 6$:

• When $x=0$, $y=6$ (point $(0,6)$)
• When $x=3$, $y = \frac{2}{3}(3)+6=8$ (point $(3,8)$)

Step3: Identify points for second line

For $y = \frac{1}{3}x + 5$:

• When $x=0$, $y=5$ (point $(0,5)$)
• When $x=3$, $y = \frac{1}{3}(3)+5=6$ (point $(3,6)$)

Step4: Find intersection of the two lines

Set the equations equal:
$\frac{2}{3}x + 6 = \frac{1}{3}x + 5$
$\frac{2}{3}x - \frac{1}{3}x = 5 - 6$
$\frac{1}{3}x = -1$
$x = -3$
Substitute $x=-3$ into $y = \frac{1}{3}x + 5$:
$y = \frac{1}{3}(-3) + 5 = -1 + 5 = 4$

Answer:

$(-3, 4)$