# How do you solve the system 2x-3y=12 and x=4y+1 by substitution?

May 21, 2015

The answer is $x = 9$ and $y = 2$.

Problem: Solve the system $2 x - 3 y = 12$ and $x = 4 y + 1$ .

$x = 4 y + 1$ is already solved for $x$. Substitute it into the other equation: $2 x - 3 y = 12$.

$2 \left(4 y + 1\right) - 3 y = 12$

Distribute the $2$.

$8 y + 2 - 3 y = 12$

Simplify.

$5 y + 2 = 12$ =

$5 y = 10$

Divide both sides by $5$.

$y = 2$

Substitute the $2$ for the $y$ into one of the original equations.

$x = 4 \cdot 2 + 1 = 9$

$x = 9$

Substitute the values for $x$ and $y$ to check the answers.

$2 x - 3 y = 12$

$2 \cdot 9 - 3 \cdot 2 = 12$

$18 - 6 = 12$

$12 = 12$

$x = 4 y + 1$

$9 = 4 \cdot 2 + 1$ =

$9 = 9$

Both equations check!