Question

1. $y=-\frac{1}{7}x-3$

$y=4$

1. $y=-\frac{2}{3}x-2$

$y=-\frac{8}{3}x+4$

Explanation:

Step1: Solve system 3: set equations equal

Set $-\frac{1}{7}x - 3 = 4$

Step2: Isolate x term

$-\frac{1}{7}x = 4 + 3$
$-\frac{1}{7}x = 7$

Step3: Solve for x

$x = 7 \times (-7)$
$x = -49$

Step4: Solve system 4: set equations equal

Set $-\frac{2}{3}x - 2 = -\frac{8}{3}x + 4$

Step5: Isolate x terms

$-\frac{2}{3}x + \frac{8}{3}x = 4 + 2$
$\frac{6}{3}x = 6$
$2x = 6$

Step6: Solve for x

$x = \frac{6}{2}$
$x = 3$

Step7: Find y for system 4

Substitute $x=3$ into $y=-\frac{2}{3}x - 2$
$y = -\frac{2}{3}(3) - 2 = -2 - 2 = -4$

Answer:

1. Solution for system 3: $(-49, 4)$
2. Solution for system 4: $(3, -4)$

To graph:

• For $y=-\frac{1}{7}x - 3$: use y-intercept $(0, -3)$ and slope $\frac{-1}{7}$; for $y=4$, draw a horizontal line at $y=4$, intersecting at $(-49, 4)$
• For $y=-\frac{2}{3}x - 2$: use y-intercept $(0, -2)$ and slope $\frac{-2}{3}$; for $y=-\frac{8}{3}x + 4$: use y-intercept $(0, 4)$ and slope $\frac{-8}{3}$, intersecting at $(3, -4)$