Question

use substitution to solve the system of equations.
$3x + 4y = -3$
$x + 2y = -1$

Explanation:

Step1: Solve the second equation for x

From \( x + 2y = -1 \), we can express \( x \) in terms of \( y \) by subtracting \( 2y \) from both sides.
\( x = -1 - 2y \)

Step2: Substitute x into the first equation

Substitute \( x = -1 - 2y \) into \( 3x + 4y = -3 \).
\( 3(-1 - 2y) + 4y = -3 \)

Step3: Simplify and solve for y

First, distribute the 3: \( -3 - 6y + 4y = -3 \)
Combine like terms: \( -3 - 2y = -3 \)
Add 3 to both sides: \( -2y = 0 \)
Divide both sides by -2: \( y = 0 \)

Step4: Substitute y back to find x

Substitute \( y = 0 \) into \( x = -1 - 2y \).
\( x = -1 - 2(0) = -1 \)

Answer:

The solution to the system of equations is \( x = -1 \) and \( y = 0 \), or the ordered pair \( (-1, 0) \).