Question

solve the system of equations graphed on the coordinate axes below.
y = -3x - 2
y = 5x + 6

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( -3x - 2 = 5x + 6 \)

Step2: Solve for \( x \)

Add \( 3x \) to both sides: \( -2 = 8x + 6 \)
Subtract 6 from both sides: \( -8 = 8x \)
Divide both sides by 8: \( x = -1 \)

Step3: Substitute \( x \) back to find \( y \)

Substitute \( x = -1 \) into \( y = 5x + 6 \): \( y = 5(-1) + 6 = -5 + 6 = 1 \)

Answer:

The solution to the system is \( x = -1 \), \( y = 1 \) or the ordered pair \( (-1, 1) \)