Question

use substitution to solve the system.

x = 3y - 14

-5x + 4y = 37

x =

y =

Explanation:

Step1: Substitute x into the second equation

We know \( x = 3y - 14 \), substitute this into \( -5x + 4y = 37 \). So we get \( -5(3y - 14)+4y = 37 \).

Step2: Simplify the equation

First, expand the left - hand side: \( - 15y+70 + 4y=37 \). Combine like terms: \( - 11y+70 = 37 \). Then subtract 70 from both sides: \( -11y=37 - 70=-33 \).

Step3: Solve for y

Divide both sides of \( -11y=-33 \) by - 11: \( y=\frac{-33}{-11} = 3 \).

Step4: Solve for x

Substitute \( y = 3 \) into \( x = 3y-14 \), we have \( x=3\times3 - 14=9 - 14=-5 \).

Answer:

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