Question

solve the system of linear equations by substitution. enter your answer as an ordered pair. \\(\

$$\begin{cases} y = -2x - 8 \\\\ y = \\frac{3}{2}x - \\frac{9}{2} \\end{cases}$$

\\) show your work here

Explanation:

Step1: Substitute y from first equation

Since both equations equal \( y \), set them equal: \( -2x - 8 = \frac{3}{2}x - \frac{9}{2} \)

Step2: Multiply by 2 to eliminate fractions

\( 2(-2x - 8) = 2(\frac{3}{2}x - \frac{9}{2}) \)
\( -4x - 16 = 3x - 9 \)

Step3: Solve for x

Add \( 4x \) to both sides: \( -16 = 7x - 9 \)
Add 9 to both sides: \( -7 = 7x \)
Divide by 7: \( x = -1 \)

Step4: Substitute x into first equation

\( y = -2(-1) - 8 = 2 - 8 = -6 \)

Answer:

\((-1, -6)\)