Question

question 18 of 40
what is the solution to the system of equations graphed below?
$y = \frac{3}{2}x + 2$
$y = -6x + 32$
graph
a. (2, 5)
b. (0, 2)
c. (8, 4)
d. (4, 8)

Explanation:

Step1: Set the equations equal

Since the solution to a system of linear equations is the point where they intersect, we set \(\frac{3}{2}x + 2=-6x + 32\).

Step2: Solve for \(x\)

First, add \(6x\) to both sides: \(\frac{3}{2}x+6x + 2=-6x+6x + 32\), which simplifies to \(\frac{3}{2}x+\frac{12}{2}x + 2 = 32\), or \(\frac{15}{2}x+2 = 32\). Then subtract 2 from both sides: \(\frac{15}{2}x=30\). Multiply both sides by \(\frac{2}{15}\): \(x = 30\times\frac{2}{15}=4\).

Step3: Solve for \(y\)

Substitute \(x = 4\) into \(y=\frac{3}{2}x + 2\): \(y=\frac{3}{2}(4)+2=6 + 2=8\).

Answer:

D. \((4, 8)\)