Question

use substitution to solve the system.
$2y + 11 = x$
$4x - 3y = 29$
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Substitute \( x \) into the second equation

We have \( x = 2y + 11 \) from the first equation. Substitute \( x \) into \( 4x - 3y = 29 \):
\( 4(2y + 11) - 3y = 29 \)

Step2: Simplify and solve for \( y \)

Expand the left - hand side:
\( 8y+44 - 3y=29 \)
Combine like terms:
\( 5y + 44=29 \)
Subtract 44 from both sides:
\( 5y=29 - 44=- 15 \)
Divide both sides by 5:
\( y=\frac{-15}{5}=-3 \)

Step3: Substitute \( y \) back to find \( x \)

Substitute \( y = - 3 \) into \( x = 2y+11 \):
\( x=2\times(-3)+11=-6 + 11 = 5 \)

Answer:

\( x = 5 \), \( y=-3 \)