Question

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

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

show your work here

Explanation:

Step1: Solve for x from the second equation

From \( x + y = -3 \), we can express \( x \) as \( x = -3 - y \).

Step2: Substitute x into the first equation

Substitute \( x = -3 - y \) into \( x - 2y = -9 \), we get \( (-3 - y) - 2y = -9 \).
Simplify the left side: \( -3 - y - 2y = -3 - 3y \). So the equation becomes \( -3 - 3y = -9 \).

Step3: Solve for y

Add 3 to both sides: \( -3y = -9 + 3 = -6 \).
Divide both sides by -3: \( y = \frac{-6}{-3} = 2 \).

Step4: Solve for x

Substitute \( y = 2 \) into \( x = -3 - y \), we get \( x = -3 - 2 = -5 \).

Answer:

\((-5, 2)\)