Add up the two equations:
2x + 5y = - 4
4x - 5y = 22
------------------
2x + 4x + 5y -+ 5y = - 4 + 22
6x = 18
x = 18 / 6
x = 3
Replace the value of x in the equation 2x + 5y = - 4
=> 2(3) + 5y = - 4
=> 5y = - 4 - 6
=> 5y = - 10
=> y = - 10 / 5
=> y = - 2
Answer: (3, - 2)
