Question

solve the system of equations graphed on the coordinate axes below.
$y = -3x + 2$
$y = \frac{1}{2}x + 2$

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other:
\( -3x + 2 = \frac{1}{2}x + 2 \)

Step2: Solve for \( x \)

Subtract \( 2 \) from both sides:
\( -3x = \frac{1}{2}x \)

Subtract \( \frac{1}{2}x \) from both sides:
\( -3x - \frac{1}{2}x = 0 \)

Combine like terms:
\( -\frac{7}{2}x = 0 \)

Multiply both sides by \( -\frac{2}{7} \):
\( x = 0 \)

Step3: Find \( y \)

Substitute \( x = 0 \) into one of the original equations (e.g., \( y = -3x + 2 \)):
\( y = -3(0) + 2 = 2 \)

Answer:

The solution to the system is \( (0, 2) \)