Question

solve the system of equations graphed on the coordinate axes below.
$y = -2x - 3$
$y = \frac{2}{3}x + 5$

Explanation:

Step1: Set the two equations equal

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

Step2: Eliminate the fraction

Multiply every term by 3 to eliminate the fraction:
\( 3(-2x - 3)=3(\frac{2}{3}x + 5) \)
\( -6x - 9 = 2x + 15 \)

Step3: Solve for \( x \)

Add \( 6x \) to both sides:
\( -9 = 8x + 15 \)
Subtract 15 from both sides:
\( -24 = 8x \)
Divide both sides by 8:
\( x=-3 \)

Step4: Substitute \( x \) back to find \( y \)

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

Answer:

The solution to the system is \( x=-3 \), \( y = 3 \) or the ordered pair \( (-3, 3) \)