Question

solve the system of equations.
y = 2x + 7
y = -3x + 2
(-5, 1)
(-3, 2)
(-1, 5)

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( 2x + 7=-3x + 2 \)

Step2: Solve for \( x \)

Add \( 3x \) to both sides: \( 2x+3x + 7=-3x+3x + 2 \), which simplifies to \( 5x + 7 = 2 \). Then subtract 7 from both sides: \( 5x+7 - 7=2 - 7 \), so \( 5x=-5 \). Divide both sides by 5: \( x=\frac{-5}{5}=-1 \)

Step3: Find \( y \)

Substitute \( x = - 1 \) into the first equation \( y = 2x+7 \): \( y=2(-1)+7=-2 + 7 = 5 \)

Answer:

\((-1, 5)\)