Solve by the method of your choice

Question

5x-4y=2

2x+y=6

 

A.) The solution is _

B.) There are infinitely many solutions

C.) There are no solutions

Answer 1

Let's try elimination:

 

      5x  - 4y = 2

     (2x +  y = 6)·4

 

     5x - 4y  =  2

     8x + 4y = 24

     ---------------

    13x + 0 = 26

 

     13x = 26

     x = 2

 

Now find y by plugging x = 2 into either original equation and solving for y:

 

     2x + y = 6

     2(2) + y = 6

     4 + y = 6

     y = 2

 

Check your answers by plugging x = 2 and y = 2 into each original equation.