Question

solve the system of equations graphed on the coordinate axes below.
y = -\frac{1}{2}x + 2
y = x - 7

Explanation:

Step1: Set equations equal

Since \( y = -\frac{1}{2}x + 2 \) and \( y = x - 7 \), set them equal: \( -\frac{1}{2}x + 2 = x - 7 \)

Step2: Solve for x

Add \( \frac{1}{2}x \) to both sides: \( 2 = \frac{3}{2}x - 7 \)
Add 7 to both sides: \( 9 = \frac{3}{2}x \)
Multiply by \( \frac{2}{3} \): \( x = 6 \)

Step3: Find y

Substitute \( x = 6 \) into \( y = x - 7 \): \( y = 6 - 7 = -1 \)

Answer:

The solution is \( (6, -1) \)