Question

solve the system by substitution.
y = -2x - 3
7x + 4y = -6
the solution is (\square, \square ).

Explanation:

Step1: Substitute \( y = -2x - 3 \) into the second equation

We have the second equation \( 7x + 4y = -6 \). Replace \( y \) with \( -2x - 3 \), so the equation becomes \( 7x + 4(-2x - 3) = -6 \).

Step2: Simplify and solve for \( x \)

First, expand \( 4(-2x - 3) \) to get \( -8x - 12 \). Then the equation is \( 7x - 8x - 12 = -6 \). Combine like terms: \( -x - 12 = -6 \). Add 12 to both sides: \( -x = 6 \). Multiply both sides by -1: \( x = -6 \).

Step3: Substitute \( x = -6 \) back into \( y = -2x - 3 \)

Calculate \( y = -2(-6) - 3 \). First, \( -2(-6) = 12 \), then \( y = 12 - 3 = 9 \).

Answer:

\((-6, 9)\)