Find the solution to the system of linear equations using elimination.

Question

Find the solution to the system of linear equations using elimination.

{−6x+8y=6

   8x−8y=0

Enter the system’s solution as an ordered pair including the parentheses and comma. If the system has no solution, enter “no solution”. If the system has infinitely many solutions, enter “infinitely many solutions”.

Answer 1

Since the y variables have the same coefficients with one being positive and one being negative

all you have to do is add the two equations together:

 

  [-6x + 8Y = 6]

+[ 8x  - 8y = 0]

______________

     2x + 0y = 6

 

2x = 6

x = 3

 

Plugging x=3 back into either original equation you get

 

 -6(3) + 8y = 6

    -18 + 8y =6

             8y = 24

               y = 3

 

Thus the ordered pair (x,y) of the solution is (3,3)