# How do you solve the system of equations 2x+3y=105 and x+2y=65?

Apr 19, 2018

$x$ equals $15$ and $y$ equals $25$.

#### Explanation:

Set the easiest equation to $x$ (the last one) and because

$x = - 2 y + 65$

the $x$ in the other equation also equals that, you can replace the $x$ in the first equation with the $- 2 y + 65$. Then simplify and solve for the $y$.

You can plug the $25$ into either equation to simplify and solve for $x$.

Looks like:

$x = - 2 y + 65$

so

$2 \left(- 2 y + 65\right) + 3 y = 105$

$- 4 y + 3 y = 105 - 130$

$y = 25$

And

$x + 2 \left(25\right) = 65$

$x = 15$