1) Eliminate X or Y by figuring out what you need to multiply one of the equations with to eliminate one of those variables when you add the equations together. So for example, to get rid of the Y variable, multiply the bottom equation by 2:
2(9x-4y=21) ---> 18x - 8y = 42
2) Add the first equatino and new second equation together:
3x+8y=32
+ 18x-8y=42
---------------------
21x = 74
3) Solve for X:
21x = 74
--- ----
21 21
x = 3.52
3) Then you plug in the X value you just figured out in step 2 into one of the equations:
3x+8y=32
3(3.52)+8y=32
10.56+8y=32
-10.56 -10.56
8y = 21.44
y = 2.68
4) Since 2/3 = 0.666 and 15/4 = 3.75 don't match what you found in the above steps, your ordered pair is not a solution of the given system.