What is the solution to this system of linear equations?

y − 4x = 7

2y + 4x = 2

(3, 1)
(1, 3)
(3, −1)
(−1, 3)

The solution to the system of linear equations is (-1,3). Here's how I got my answer step by step using the substitution method.

Step 1: Solve for either x or y in one of the two equations.
  
    y  -  4x  =  7
        + 4x   + 4x

    y = 4x + 7

Step 2: Plug in the value that you got for x or y into the equation that you haven't worked with yet.

2(4x + 7) + 4x = 2
8x + 14 + 4x = 2
     
 12x  +  14  =  2
          - 14   - 14

 12x = -12
 
  12      12

    x = -1

Step 3: Plug in the number you got for y or x into either of the two equations.

  y - 4(-1) = 7 
  y  +  4  =  7  
        - 4    - 4

  y = 3

The final answer is (-1,3). If you want to check to make sure that this coordinate is a solution to the system of equations, all you have to do is plug in -1 for x and 3 for y into both equations. 

Equation 1: y - 4x = 7
Equation 2: 2y + 4x = 2

3 - 4(-1) = 7                      2(3) + 4(-1) = 2
3 + 4 = 7                           6 - 4 = 2
7 = 7                                  2 = 2

I hope all of this makes sense to you :)