Question

solve each system of equations by graphing

1. $y = x + 4$

$y = -2x - 2$

Explanation:

Step1: Find intersection algebraically

Set $x + 4 = -2x - 2$

Step2: Solve for $x$

$x + 2x = -2 - 4$
$3x = -6$
$x = -2$

Step3: Find $y$ value

Substitute $x=-2$ into $y=x+4$:
$y = -2 + 4 = 2$

Step4: Verify on graph

Plot $y=x+4$ (y-intercept $(0,4)$, slope $1$) and $y=-2x-2$ (y-intercept $(0,-2)$, slope $-2$). The lines intersect at $(-2,2)$.

Answer:

The solution to the system is $(-2, 2)$