Question

solve the following system of equations graphically on the set of axes below.
$y = -2x - 8$
$y = \frac{2}{3}x + 8$
plot two lines by clicking the graph.
click a line to delete it.
graph with x-axis from -10 to 10 and y-axis from -10 to 10
answer attempt 1 out of 2
solution: input box submit answer

Explanation:

Step1: Find intercepts for $y=-2x-8$

For y-intercept, set $x=0$:
$y=-2(0)-8=-8$ → Point $(0, -8)$
For x-intercept, set $y=0$:
$0=-2x-8 \implies 2x=-8 \implies x=-4$ → Point $(-4, 0)$

Step2: Find intercepts for $y=\frac{2}{3}x+8$

For y-intercept, set $x=0$:
$y=\frac{2}{3}(0)+8=8$ → Point $(0, 8)$
For x-intercept, set $y=0$:
$0=\frac{2}{3}x+8 \implies \frac{2}{3}x=-8 \implies x=-8\times\frac{3}{2}=-12$ (use $x=-3$ for integer point: $y=\frac{2}{3}(-3)+8=6$ → Point $(-3, 6)$)

Step3: Solve algebraically for intersection

Set equations equal:
$-2x-8=\frac{2}{3}x+8$
Multiply all terms by 3 to eliminate fraction:
$-6x-24=2x+24$
Rearrange terms:
$-6x-2x=24+24$
$-8x=48$
$x=-6$
Substitute $x=-6$ into $y=-2x-8$:
$y=-2(-6)-8=12-8=4$

Answer:

The solution (intersection point) is $(-6, 4)$