Question

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

Explanation:

Step1: Set the two equations equal

Since both equations equal $y$, we set $-\frac{3}{2}x + 8=x + 8$.

Step2: Solve for $x$

Subtract $x$ from both sides: $-\frac{3}{2}x-x+8=x - x+8$, which simplifies to $-\frac{3}{2}x-\frac{2}{2}x+8 = 8$, then $-\frac{5}{2}x+8 = 8$. Subtract 8 from both sides: $-\frac{5}{2}x+8 - 8=8 - 8$, getting $-\frac{5}{2}x=0$. Multiply both sides by $-\frac{2}{5}$: $x = 0$.

Step3: Solve for $y$

Substitute $x = 0$ into $y=x + 8$. So $y=0 + 8=8$.

Answer:

$x = 0,y = 8$