Question

solve the system of equations graphed on the coordinate axes below.
y = 2x + 8
y = -x + 8

Explanation:

Step1: Set the two equations equal

Since \(y = 2x + 8\) and \(y=-x + 8\), we set \(2x+8=-x + 8\).

Step2: Solve for x

Add \(x\) to both sides: \(2x+x+8=-x+x + 8\), which simplifies to \(3x+8 = 8\). Then subtract 8 from both sides: \(3x+8 - 8=8 - 8\), getting \(3x=0\). Divide both sides by 3: \(x = 0\).

Step3: Solve for y

Substitute \(x = 0\) into \(y=-x + 8\), so \(y=-0 + 8=8\).

Answer:

\(x = 0,y = 8\)