Question

solve the system of equations graphed on the coordinate axes below.
$y = \frac{1}{2}x + 8$
$y = -4x + 8$

Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( \frac{1}{2}x + 8 = -4x + 8 \).

Step2: Solve for \( x \)

Subtract 8: \( \frac{1}{2}x = -4x \).
Add \( 4x \): \( \frac{1}{2}x + 4x = 0 \) → \( \frac{9}{2}x = 0 \) → \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y = \frac{1}{2}x + 8 \): \( y = 8 \).

Answer:

The solution is \( (0, 8) \)