# How do you solve the system #-4x-15y=-17# and #-x+5y=-13#?

##### 1 Answer

You can solve it by several methods, let's see them:

Take a variable and separate it, in this case will be easier if we take the

Now we replace the

So now we have a one variable equation which is easy to solve:

Now we've got the

You can solve the system by separating the same variable in each equation and matching them, we've seen before:

And in the other one:

We match them and we get:

And now we solve the one variable equation:

Replace that

Instead of those two methods, you can reduce the system, if you don't know how to reduce a matrix by Gauss' method, you just need to multiply one or both equations by a number which, the sum of those will result 0 for one variable, let's see it:

If you now sum this equation to the other one, you will notice that:

Which gives again

Any of these methods will give you the same result in case the system has a unique solution, and of course you can apply the method swapping the variables, isolating y, or reducing y or whatever.