Question

solve the following system of equations graphically on the set of axes below.
$y = x + 8$
$y = -2x - 4$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=x+8$

• y-intercept: When $x=0$, $y=0+8=8$, so point $(0, 8)$.
• x-intercept: When $y=0$, $0=x+8 \implies x=-8$, so point $(-8, 0)$.

Step2: Find intercepts for $y=-2x-4$

• y-intercept: When $x=0$, $y=-2(0)-4=-4$, so point $(0, -4)$.
• x-intercept: When $y=0$, $0=-2x-4 \implies 2x=-4 \implies x=-2$, so point $(-2, 0)$.

Step3: Graph lines and find intersection

Plot the two lines using their intercepts. To find the intersection algebraically (to confirm):
Set $x+8 = -2x-4$
$x+2x = -4-8$
$3x = -12$
$x = -4$
Substitute $x=-4$ into $y=x+8$: $y=-4+8=4$
Intersection point is $(-4, 4)$.

Answer:

The solution to the system is the point of intersection: $\boldsymbol{(-4, 4)}$
(To graph: Plot $(0,8)$ and $(-8,0)$ then draw a line through them for $y=x+8$; plot $(0,-4)$ and $(-2,0)$ then draw a line through them for $y=-2x-4$; the lines cross at $(-4,4)$.)