3x+4y=-1, -9x-4y=-1

Nice and simple really.
Make x the subject in one of the equations then plug that value into the second.

Homework?

First, tell us what the eliminations method is, then you'll see that the answer is right there.

Well I don't really know because this is the first time I've ever seen this problem...

Ok, by example:

4x + 3y = -5
2x - y = 5

Using the elimination method you multiple the second equation (both sides of it) by 3. This will make the -y in the second become -3y, so that when you add the two equations together, the y terms will cancel out.

Multiplying both sides of second equation by 3...
3(2x - y) = 3 x 5 => 6x - 3y = 15

This results in this pair of equations

4x + 3y = -5 <= the original first equation
6x - 3y = 15 <= new second equation

Adding them together (3y + -3y = 0)...

10x = 10

And thus x = 1

To solve for y, plug x=1 into the first equation (you could choose the second equation, just pick what looks easier)

4 + 3y = -5
3y = -9
y=3


So, in the elimination method, your goal is to get rid of one of the variables by multiplying or dividing one of the equations by a constant value and then adding the two equations together. If the equations already have equal but opposite terms, just add them together and solve for the remaining variable.