Hey guys I'm having some trouble with this question, can someone walk me through this, please help me. Which ordered pair (x, y) satisfies the system of equations shown below?
2x-y=6
x+2y=-2
A) (-6,2)
B) (-2,2)
C)(2,-2)
D) (4,2)

Explanation:

equation 1.       2x-y=6

equation  2.     x+2y= -2

To eliminate the terms with x, we have to make the x in equation 2    become -2x

so multiply equation 2 by -2

Equation 1.     2x-y =6

equation 2.   -2( x + 2y =  -2)  =  -2x - 4y = 4

equation 1.     2x-y = 6

equation 2.     -2x - 4y = 4

cancel out the 2x and -2x in equatins 1 and 2 so we can solve for y

then we have -5y  = 10

                                                       y =  -2

Now substitute for -2 for y in any previous equation

Let's use equation 1

2x - (-2) = 6

2x +2 =6

2x = 4

x = 2

Answer  :   x =2, Y = -2