# How do you solve 2x+5y=3 and x-3y=7?

Sep 28, 2015

The system has a solution:

$\left\{\begin{matrix}x = 4 \\ y = - 1\end{matrix}\right.$

#### Explanation:

$\left\{\begin{matrix}2 x + 5 y = 3 \\ x - 3 y = 7\end{matrix}\right.$

First we multiply the second equation by $- 2$

$\left\{\begin{matrix}2 x + 5 y = 3 \\ - 2 x + 6 y = - 14\end{matrix}\right.$

Now we can add the equations to get an equation with one unknown only:

$11 y = - 11$

Now we can calculate, that $y = - 1$

If we substitute the value of $y$ to the 2nd equation we get:

$x + 3 = 7$

So $x = 4$

Finally we can write the solution:

$\left\{\begin{matrix}x = 4 \\ y = - 1\end{matrix}\right.$