SOLUTION: -2x+3y=14 x+2y=7

-2x + 3y = 14,   (1)
  x + 2y =  7.   (2)

To solve this system, multiply the equation (2) by 2 and then add to the equation (1). 
In this way, you eliminate the unknown x and get a single equation for the unknown y:

3y + 4y = 14 + 2*7,   or

7y = 28,

y =  = 4.

You just found y. Now substitute the value y = 4 into equation (2) and get

x + 2*4 = 7.

Hence x = 7 - 8 = -1.