Question

(04.02 mc) solve the system of equations. x + 3y = -1 2x + 2y = 6 (-4, 1) (2, -1) (4, -1) (5, -2)

Explanation:

Step1: Solve for x from the first equation

From \( x + 3y = -1 \), we get \( x = -1 - 3y \).

Step2: Substitute x into the second equation

Substitute \( x = -1 - 3y \) into \( 2x + 2y = 6 \):
\( 2(-1 - 3y) + 2y = 6 \)
\( -2 - 6y + 2y = 6 \)
\( -2 - 4y = 6 \)

Step3: Solve for y

Add 2 to both sides: \( -4y = 8 \)
Divide by -4: \( y = -2 \)

Step4: Solve for x

Substitute \( y = -2 \) into \( x = -1 - 3y \):
\( x = -1 - 3(-2) = -1 + 6 = 5 \)

Answer:

(5, -2)