Question

1. $\begin{cases} y = \frac{2}{3}x + 3 \\ y = -2x - 5 end{cases}$

solution:

Explanation:

Step1: Set equations equal

$\frac{2}{3}x + 3 = -2x - 5$

Step2: Eliminate fraction, multiply by 3

$2x + 9 = -6x - 15$

Step3: Isolate x terms

$2x + 6x = -15 - 9$

Step4: Simplify to solve for x

$8x = -24 \implies x = -3$

Step5: Substitute x to find y

$y = -2(-3) - 5 = 6 - 5 = 1$

Answer:

The solution to the system is $(-3, 1)$

To graph:

1. For $y=\frac{2}{3}x+3$: plot the y-intercept $(0,3)$, then use slope $\frac{2}{3}$ (rise 2, run 3) to plot another point, draw the line.
2. For $y=-2x-5$: plot the y-intercept $(0,-5)$, then use slope $-2$ (rise -2, run 1) to plot another point, draw the line.

The lines intersect at $(-3, 1)$.