Question

How to solve this system by substitution: -4x-2y=-14 and 2x+y=7

Answer 1

      Yay! I'm so glad that this system of linear equations has to be solved by substitution because it is my favorite way to solve these kinds of problems. I will explain how to do this problem step by step, just like I learned in 8th grade. I hope this makes sense to you :)

Step 1:  Solve for either x or y in one of the two equations.

      -4x - 2y = -14
    + 4x          + 4x
---------------------------
       -2y = 4x - 14
     ------  ------ ------
       -2     -2     -2 
         
        y = 2x + 7

Step 2: Plug in the solution you got for x or y into the equation you have not worked with yet. (2x + y = 7)

2x + 2x + 7 = 7      ⇒       4x + 7 = 7
                                                - 7  - 7
                                      --------------------
                                          4x = 0
                                        -----  -----
                                          4      4
                           
                                           x = 0

Step 3: Plug in the solution you got in step 2 into either of the 2 equations.

2(0) + y = 7      ⇒      0 + y = 7
                                 - 0        - 0
                            ----------------------
                                   y = 7

The final solution to a systems of linear equations is written in a coordinate pair. (x,y)

In your case, the final answer would be (0, 7).