Question

use substitution to solve the system.
3x + 5y = 25
2x - 8 = y
x =

y =

Explanation:

Step1: Substitute \( y = 2x - 8 \) into \( 3x + 5y = 25 \)

Substitute \( y \) in the first equation: \( 3x + 5(2x - 8) = 25 \)

Step2: Simplify and solve for \( x \)

Expand the equation: \( 3x + 10x - 40 = 25 \)
Combine like terms: \( 13x - 40 = 25 \)
Add 40 to both sides: \( 13x = 25 + 40 \)
\( 13x = 65 \)
Divide by 13: \( x = \frac{65}{13} = 5 \)

Step3: Substitute \( x = 5 \) into \( y = 2x - 8 \)

\( y = 2(5) - 8 = 10 - 8 = 2 \)

Answer:

\( x = 5 \)
\( y = 2 \)