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 set \( -3x + 2=\frac{1}{2}x + 2 \).

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: \( -\frac{6}{2}x-\frac{1}{2}x = 0\Rightarrow-\frac{7}{2}x = 0 \).
Multiply both sides by \( -\frac{2}{7} \): \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y=-3x + 2 \): \( y=-3(0)+2 = 2 \).

Answer:

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