Question

solve the system by substitution.

( x = -2y + 5 )
( -8x - 3y = -1 )

Explanation:

Step1: Substitute \( x = -2y + 5 \) into the second equation

We have the second equation \( -8x - 3y = -1 \). Replace \( x \) with \( -2y + 5 \):
\( -8(-2y + 5) - 3y = -1 \)

Step2: Simplify and solve for \( y \)

First, distribute the -8:
\( 16y - 40 - 3y = -1 \)
Combine like terms:
\( 13y - 40 = -1 \)
Add 40 to both sides:
\( 13y = 39 \)
Divide both sides by 13:
\( y = 3 \)

Step3: Substitute \( y = 3 \) back into \( x = -2y + 5 \)

\( x = -2(3) + 5 \)
\( x = -6 + 5 \)
\( x = -1 \)

Answer:

The solution to the system is \( x = -1 \), \( y = 3 \)