2x-9y=-25 -4x-9y=-23 system with elimination

Multiply the first equation by -2. It turns into 4x+18y=50 and the other one stays -4x-9y=-23. Then you "eliminate" the equations by "adding" them. Set it up like this: 
4x+18y=50
      +
-4x-9y=-23
4x-4x= 0. 18y-9y= 9y and 50-23= 27
SO: 9y= 27 and y= 3
And then you plug that in to one equation: 4x +18(3)= 50. 4x= 50-(18*3)
4x= -4, so x=-1.
Plug it back in to check! 
Hope this helps. Happy solving! :)

Tyw23456 explained it quite masterfully, but here is another way to solve the system. Start by multiplying one equation by -1 so later when we add them, the like terms with variable y will be eliminated so we can solve for x:

-1(-2x - 9y = -25) → (2x + 9y = 25)

Now add the equations (we can factor a -1 out of the bottom equation for a subtraction problem):

    2x + 9y = 25
- (4x + 9y = 23)

  -2x        =    2

Now solve for x:

-2x = 2

x = -1

Now we can plug this value back into one of the original equations to solve for y:

-2(-1) - 9y = -25

2 - 9y = -25

-9y = -27

y = 3