Question

solve the system of equations graphed on the coordinate axes below.
$y = -\frac{3}{2}x - 7$
$y = 2x$

Explanation:

Step1: Set the equations equal

Since \( y = 2x \) and \( y = -\frac{3}{2}x - 7 \), substitute \( y \) from the second equation into the first: \( 2x = -\frac{3}{2}x - 7 \)

Step2: Solve for x

Multiply all terms by 2 to eliminate the fraction: \( 4x = -3x - 14 \)
Add \( 3x \) to both sides: \( 7x = -14 \)
Divide by 7: \( x = -2 \)

Step3: Find y

Substitute \( x = -2 \) into \( y = 2x \): \( y = 2(-2) = -4 \)

Answer:

The solution is \( x = -2 \), \( y = -4 \) or the ordered pair \( (-2, -4) \)