Question

solve the system of equations.
3x + 4y = -23
x = 3y + 1
x =

y =
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Explanation:

Step1: Substitute \( x = 3y + 1 \) into \( 3x + 4y = -23 \)

We know that \( x \) is equal to \( 3y + 1 \), so we replace \( x \) in the second equation with \( 3y + 1 \). This gives us \( 3(3y + 1) + 4y = -23 \).

Step2: Expand and simplify the equation

First, expand \( 3(3y + 1) \) to get \( 9y + 3 \). Then the equation becomes \( 9y + 3 + 4y = -23 \). Combine like terms: \( 9y + 4y = 13y \), so \( 13y + 3 = -23 \).

Step3: Solve for \( y \)

Subtract 3 from both sides: \( 13y = -23 - 3 = -26 \). Then divide both sides by 13: \( y = \frac{-26}{13} = -2 \).

Step4: Solve for \( x \) using \( x = 3y + 1 \)

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

Answer:

\( x = -5 \), \( y = -2 \)