# How do you find the solution of the system of equations x+2y=5 and 2x-3y=-4?

May 21, 2015

The answer is $x = 5 - 2 y$ and $y = 2$

Problem: Solve the system of equations $x + 2 y = 5$ and $2 x - 3 y = - 4$.

First equation. Solve for $x$.

$x + 2 y = 5$

Subtract $2 y$ from both sides.

$x = 5 - 2 y$

Second equation. Solve for $y$.

Substitute $5 - 2 y$ for $x$ in the other equation. Solve for $y$.

$2 x - 3 y = - 4$ =

$2 \left(5 - 2 y\right) - 3 y = - 4$

Distribute the $2$.

$10 - 4 y - 3 y = - 4$

Combine like terms.

$- 7 y + 10 = - 4$ =

$- 7 y = - 14$

Divide both sides by $- 7$.

$y = 2$

Check your answers by substituting the values for $x$ and $y$ back into both of the original equations.

$x + 2 y = 5$ =

$5 - 2 \cdot 2 + 2 \cdot 2 = 5$ =

$5 - 4 + 4 = 5$ =

$5 = 5$

$2 x - 3 y = - 4$ =

$2 \left(5 - 2 \cdot 2\right) - 3 \cdot 2 = - 4$

Distribute the $2$.

$10 - 8 - 6 = - 4$ =

$- 4 = - 4$