Question

graph the system of equations.\

$$\begin{cases}6x - 4y = -24\\\\4x - 8y = -32\\end{cases}$$

\
use the line tool to graph the lines.

Explanation:

Step1: Rewrite to slope-intercept form

For $6x - 4y = -24$:
Subtract $6x$: $-4y = -6x -24$
Divide by $-4$: $y = \frac{3}{2}x + 6$

For $4x - 8y = -32$:
Subtract $4x$: $-8y = -4x -32$
Divide by $-8$: $y = \frac{1}{2}x + 4$

Step2: Identify intercepts for first line

x-intercept (set $y=0$):
$0 = \frac{3}{2}x + 6 \implies \frac{3}{2}x = -6 \implies x = -4$ → Point $(-4, 0)$
y-intercept (set $x=0$):
$y = 6$ → Point $(0, 6)$

Step3: Identify intercepts for second line

x-intercept (set $y=0$):
$0 = \frac{1}{2}x + 4 \implies \frac{1}{2}x = -4 \implies x = -8$ → Point $(-8, 0)$
y-intercept (set $x=0$):
$y = 4$ → Point $(0, 4)$

Answer:

1. For the line $y = \frac{3}{2}x + 6$, plot the points $(-4, 0)$ and $(0, 6)$, then draw a straight line through them.
2. For the line $y = \frac{1}{2}x + 4$, plot the points $(-8, 0)$ and $(0, 4)$, then draw a straight line through them.