What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32

There are two ways to solve a system of linear equations. Substitution and elimination. I do substitution better. 
First solve one of the equations for either x or y. 
y= 32 - 5x (if you solve for y for the second equation)
Then substitute this equation into the first equation for the value of y:
3x - 2(32 - 5x)= 14
Then solve for x:
3x - 2(32 - 5x) =14
3x - 64 + 10x = 14
13x - 64 = 14
13x = 78
x = 6 
Then, plug the value of x into the original second equation:
5(6) + y = 32
30 + y = 32
y = 2
Then you have your solution. Hope this helps!