Question

question
solve the system of equations graphed on the coordinate axes below.
$y = -\frac{3}{2}x + 8$
$y = x + 8$

Explanation:

Step1: Set equations equal

Since $y = y$, equate the two expressions:
$$x + 8 = -\frac{3}{2}x + 8$$

Step2: Isolate x terms

Subtract 8 from both sides:
$$x = -\frac{3}{2}x$$
Add $\frac{3}{2}x$ to both sides:
$$x + \frac{3}{2}x = 0$$
$$\frac{2}{2}x + \frac{3}{2}x = 0$$
$$\frac{5}{2}x = 0$$

Step3: Solve for x

Multiply both sides by $\frac{2}{5}$:
$$x = 0 \times \frac{2}{5}$$
$$x = 0$$

Step4: Find y value

Substitute $x=0$ into $y = x + 8$:
$$y = 0 + 8$$
$$y = 8$$

Answer:

The solution is $(0, 8)$