Question

solve the system of equations graphed on the coordinate axes below.
$y = -2x - 1$
$y = 3x + 4$

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( -2x - 1 = 3x + 4 \)

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( -1 = 5x + 4 \)
Subtract \( 4 \) from both sides: \( -5 = 5x \)
Divide both sides by \( 5 \): \( x = -1 \)

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

Substitute \( x = -1 \) into one of the original equations, say \( y = 3x + 4 \): \( y = 3(-1) + 4 = -3 + 4 = 1 \)

Answer:

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