Question

graph the system of equations.\

$$\begin{cases}8x + 8y = 64\\\\2x - 2y = -4\\end{cases}$$

\
use the line tool to graph the lines.

Explanation:

Step1: Rewrite first equation to slope-intercept form

Divide by 8, solve for $y$:
$8x + 8y = 64 \implies x + y = 8 \implies y = -x + 8$

Step2: Find intercepts for first line

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

Step3: Rewrite second equation to slope-intercept form

Divide by 2, solve for $y$:
$2x - 2y = -4 \implies x - y = -2 \implies y = x + 2$

Step4: Find intercepts for second line

• x-intercept (set $y=0$): $0 = x + 2 \implies x=-2$, point $(-2, 0)$
• y-intercept (set $x=0$): $y = 0 + 2 \implies y=2$, point $(0, 2)$

Step5: Solve for intersection point

Set equations equal: $-x + 8 = x + 2$
$\implies -2x = -6 \implies x=3$
Substitute $x=3$: $y = 3 + 2 = 5$, point $(3, 5)$

Answer:

1. For $y = -x + 8$: Plot points $(0, 8)$ and $(8, 0)$, draw a line through them.
2. For $y = x + 2$: Plot points $(0, 2)$ and $(-2, 0)$, draw a line through them.
3. The lines intersect at $(3, 5)$.