Question

solve the system by substitution.
$5x - 6y = -4$
$x = 7y + 5$
the solution is (\square, \square).

Explanation:

Step1: Substitute \( x = 7y + 5 \) into \( 5x - 6y = -4 \)

Substitute \( x \) in the first equation with \( 7y + 5 \):
\( 5(7y + 5) - 6y = -4 \)

Step2: Simplify and solve for \( y \)

Expand the left - hand side:
\( 35y + 25 - 6y = -4 \)
Combine like terms:
\( 29y + 25 = -4 \)
Subtract 25 from both sides:
\( 29y = -4 - 25 \)
\( 29y = -29 \)
Divide both sides by 29:
\( y = - 1 \)

Step3: Substitute \( y=-1 \) into \( x = 7y + 5 \) to find \( x \)

\( x = 7\times(-1)+5 \)
\( x=-7 + 5 \)
\( x=-2 \)

Answer:

\((-2,-1)\)