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

Step2: Solve for x

Subtract 8 from both sides: \( \frac{1}{2}x = -4x \). Add \( 4x \) to both sides: \( \frac{1}{2}x + 4x = 0 \). Combine terms: \( \frac{9}{2}x = 0 \), so \( x = 0 \).

Step3: Find y

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

Answer:

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