Question

use substitution to solve the system.
y = 2x + 11
-3x + 5y = 27
x =
y =

Explanation:

Step1: Substitute \( y = 2x + 11 \) into the second equation

We have the second equation \( -3x + 5y = 27 \). Substitute \( y \) with \( 2x + 11 \), so the equation becomes \( -3x + 5(2x + 11) = 27 \).

Step2: Simplify and solve for \( x \)

First, expand \( 5(2x + 11) \) to get \( 10x + 55 \). Then the equation is \( -3x + 10x + 55 = 27 \). Combine like terms: \( 7x + 55 = 27 \). Subtract 55 from both sides: \( 7x = 27 - 55 = -28 \). Divide both sides by 7: \( x = \frac{-28}{7} = -4 \).

Step3: Substitute \( x = -4 \) back into \( y = 2x + 11 \) to find \( y \)

Substitute \( x = -4 \) into \( y = 2x + 11 \), we get \( y = 2(-4) + 11 = -8 + 11 = 3 \).

Answer:

\( x = -4 \), \( y = 3 \)