Algebra 2 Elimination

this question really does not lend itself to elimination method but here it is.
This is just one way to go about elimination, there are other ways you could have gone about this.

multilply the first one by 2 and swap sides

2(-5/7-11/7*x)=-y*2
-10/7 - 22x/7 = -2y
-2y = -10/7 - 22x/7
So now the equations are

-2y = -10/7 - 22x/7 and
+2y = 7+5x

now add
-2y+2y = -10/7 + 7 - 22x/7 +5x
0 = -10/7 + 7 - 22x/7 +5x

It is easier now just to multiply everything by 7 and then to solve for x
Once you solve for x substitute it back into one of the original equations to get y.

thanks a lot Sidney I found a little thing called Matrix and learned a little bit more about elimination but thanks for the help.

Yes,
Matrices can be very useful.
I don't usually solve little equations that way.
But they are extremely useful when you have several equations with several unknowns.