Question

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

Explanation:

Step1: Set the two equations equal

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

Step2: Multiply through by 2 to eliminate fraction

Multiply each term by 2:
\( 2(-3x - 2)=2(\frac{3}{2}x + 7) \)
\( -6x - 4 = 3x + 14 \)

Step3: Move all x terms to one side

Add \( 6x \) to both sides:
\( -4=9x + 14 \)

Step4: Solve for x

Subtract 14 from both sides:
\( -18 = 9x \)
Divide by 9:
\( x=-2 \)

Step5: Substitute x back to find y

Substitute \( x = -2 \) into \( y=-3x - 2 \):
\( y=-3(-2)-2 \)
\( y = 6 - 2 \)
\( y = 4 \)

Answer:

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