Question

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

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \(\frac{1}{2}x + 8=-4x + 8\)

Step2: Solve for \( x \)

Subtract 8 from both sides: \(\frac{1}{2}x=-4x\)
Add \( 4x \) to both sides: \(\frac{1}{2}x + 4x = 0\)
Convert \( 4x \) to halves: \(\frac{1}{2}x+\frac{8}{2}x = 0\)
Combine like terms: \(\frac{9}{2}x = 0\)
Multiply both sides by \(\frac{2}{9}\): \(x = 0\)

Step3: Find \( y \)

Substitute \( x = 0 \) into one of the equations, say \( y=-4x + 8\): \(y=-4(0)+8 = 8\)

Answer:

\((0, 8)\)