Substitute the 2x-10 in for I in the first equation: 
5x+4(2x-10) =12 
Distribute the 4:
5x+8x-40=12 
Add 40 to both sides and combine the x terms: 
13x=52
Divide by 13:
x=4 
Plug the 4 into either equation for the x value: 
y=2(4)-10 
y=8-10 
y=-2
Answer: 
X=4 
Y=-2 
To check you can plug them into either one of the equations.