Question

solve the system by substitution.
y = -3x - 7
5x - 7y = -3
the solution is (\square, \square ).

Explanation:

Step1: Substitute \( y = -3x - 7 \) into \( 5x - 7y = -3 \)

We replace \( y \) in the second equation with \( -3x - 7 \). So the equation becomes \( 5x - 7(-3x - 7) = -3 \).

Step2: Simplify and solve for \( x \)

First, distribute the -7: \( 5x + 21x + 49 = -3 \). Then combine like terms: \( 26x + 49 = -3 \). Subtract 49 from both sides: \( 26x = -3 - 49 = -52 \). Divide both sides by 26: \( x = \frac{-52}{26} = -2 \).

Step3: Substitute \( x = -2 \) into \( y = -3x - 7 \) to find \( y \)

Plug \( x = -2 \) into the first equation: \( y = -3(-2) - 7 = 6 - 7 = -1 \).

Answer:

\((-2, -1)\)