If x+2y=8 and x/2-Y=10, then x=?

Question

If x+2y=8 and x/2-Y=10, then x=?

Find x

Answer 1

You may solve this either by Substitution or by Elimination.

 

Substitution:

    To eventually solve for x, first solve for y in one equation and substitute that into other equation.

      x/2 - y = 10

        -y = -x/2 + 10

        y = x/2 - 10

 

    x + 2y = 8

    x + 2(x/2 - 10) = 8

    x + x -20 = 8

      2x - 20 = 8

      2x = 28

       x = 14

 

Elimination:

    Get the same coefficient for the variable to be eliminated, then add/subtract equations.

          x   +  2y  = 8

    (1/2)x  - y   = 10

 Multiply second equation by 2:

        x    +  2y    =   8

        x    -   2y    = 20

-----------------------------   (elimination; add equations)

      2x               = 28

             x = 14

Answer 2

1. Get rid of the fraction in the second equation by multiplying every term by the denominator.

 

2(x) - 2y =2(10) 

   2

 

x - 2y = 20

 

2. Solve Step 1 for x

x = 2y + 20

 

3. Substitute Step 2 into the remaining original equation

(2y + 20) + 2y = 8

 

4. Simplify

4y + 20 = 8

 

5. Solve for "y"

 

6. Plug "y" into x + 2y = 8 to get "x"