First, change one of the equations to an y=x form I'll use the top one for example.
3x-2y=14
-2y=14-3x
y=-7+(3/2)x
Not that you can show what y is in terms of x, plug in the x side of the equation into the other equation, for y.
x+2(-7+(3/2)x)=10
Now, you can solve for x
x-14+3x=10
4x-14=10
4x=24
x=6
Using this value of x, we can now solve for y using one of the original equations.
(6)+2y=10
2y=4
y=2
