What is the solution to the system of linear i equalities 3x-2y=14 5x+y=32

3x-2y=14
5x+y=32

there are a couple of ways to solve this but I am going to eliminate one of the variables.
First, multiply the second equation by 2

2(5x+y=32)
10x+2y=64

now, we add the first equation with the second, which will eliminate the y value

3x-2y=14
10x+2y=64

13x=78

now we can solve for x

13x=78
x=6

now that we have the value for x, we can plug in 6 for the x value in either equation and solve for y

5x+y=32
5(6)+y=32
30+y=32
y=2

we can check to make sure our values are right by plugging them back into both equations to make sure we get the right answer

3(6)-2(2)=14
18-4=14
14=14

5(6)+2=32
30+2=32
32=32

hope this helped