Question

5x + 2y = 7
–2x + 2y = –14

Answer 1

First, we're going to get one of the equations in terms of one of the variables

-2x+2y=-14 ---> 2y=-14+2x ---> y=-7+x

we can now plug that in as our y value in our other equation

5x+2(-7+x)=7

now we will solve that equation for our x value

5x+2(-7-x)=7 ---> 5x-14+2x=7 ---> 7x-14=7 ---> 7x=21 ---> x=3

we can now plug this numeric value back into the equation in order to solve for our y variable

5(3)+2y=7 ---> 15+2y=7 ---> 2y=-8 ---> y=-4

Answer 2

5x + 2y = 7....multiply by -1
-2x + 2y = -14
----------------
-5x - 2y = -7 (result of multiplying by -1)
-2x + 2y = -14
---------------add
-7x = - 21
x = -21/-7
x = 3

5x + 2y = 7
5(3) + 2y = 7
15 + 2y = 7
2y = 7 - 15
2y = - 8
y = -8/2
y = -4

solution is (3,-4)