Solve using Elimination

Question

Solve Using Elimination: x+2y=10

                                   2x+3y=14

Answer 1

To use elimination to get rid of x:

       ( 2x + 4y = 20  )    (eq1 * 2)

     - ( 2x + 3y = 14 )

      ------------------   (subtract second equation from first)

                   y = 6

 

Now, let's use elimination again to get rid of y:

       - ( 3x + 6y = 30 )   (eq1 * 3)

         ( 4x + 6y = 28 )   (eq2 * 2)

           ----------------    (subtract first equation from second)

            x          = -2

Answer 2

x+2y=10
2x+3y=14

 

Multiply the first equation by 2 so when we subtract the second equation the x's eliminate each other.

    2(x+2y=10)
-  2x+3y=14

 

    2x+4y=20
-  2x+3y=14

 

y=6

 

Plug in y to either equation then solve for x.

x+2y=10

x+2(6)=10

x+12=10

x=-2