# How do you solve the system of equations -8x + 3y = 7 and 13x - 3y = - 17?

Apr 28, 2017

See explanation.

#### Explanation:

The starting system can be written as:

## $\left\{\begin{matrix}- 8 x + 3 y = 7 \\ 13 x - 3 y = - 17\end{matrix}\right.$

We can see that the coefficients of $y$ are opposite numbers, so if we add both sides of the equations we get rid of one variable:

## $5 x = - 10 \implies x = - 2$

Now if we substitute the calculated value of $x$ to any of the equations we can calculate the remaining variable $y$:

## $- 3 y = - 9 \implies y = - 3$

Finally we can write that the solution is: