Question

solve the system by substitution.
$6y - 7 = x$
$3x - 8y = -31$
answer attempt 1 out of a
(□,□) submit answer

Explanation:

Step1: Substitute \( x = 6y - 7 \) into the second equation

We have the second equation \( 3x - 8y = -31 \). Replace \( x \) with \( 6y - 7 \):
\( 3(6y - 7) - 8y = -31 \)

Step2: Simplify and solve for \( y \)

First, distribute the 3: \( 18y - 21 - 8y = -31 \)
Combine like terms: \( 10y - 21 = -31 \)
Add 21 to both sides: \( 10y = -31 + 21 = -10 \)
Divide both sides by 10: \( y = \frac{-10}{10} = -1 \)

Step3: Substitute \( y = -1 \) back into \( x = 6y - 7 \) to find \( x \)

\( x = 6(-1) - 7 = -6 - 7 = -13 \)

Answer:

\((-13, -1)\)