Question

solve the system of equations graphed on the coordinate axes below.
y = \frac{3}{2}x + 6
y = -\frac{1}{2}x - 6

Explanation:

Step1: Set equations equal

Since \( y = \frac{3}{2}x + 6 \) and \( y = -\frac{1}{2}x - 6 \), set \( \frac{3}{2}x + 6 = -\frac{1}{2}x - 6 \).

Step2: Solve for x

Add \( \frac{1}{2}x \) to both sides: \( \frac{3}{2}x + \frac{1}{2}x + 6 = -6 \) → \( 2x + 6 = -6 \).
Subtract 6: \( 2x = -12 \) → \( x = -6 \).

Step3: Find y

Substitute \( x = -6 \) into \( y = \frac{3}{2}x + 6 \):
\( y = \frac{3}{2}(-6) + 6 = -9 + 6 = -3 \).

Answer:

The solution is \( x = -6 \), \( y = -3 \) (or the point \((-6, -3)\)).