Use the elimination method to solve the system of equations. 5x + 2y = 7 −5x + 4y = 5 ( 35, 2) there are an infinite number of solutions. (2, 1) there is no solution.

5x + 2y = 7
-5x + 4y = 5

You can immediately eliminate the x-terms and subtract:

  2y = 7
  4y = 5
-
-2y = 2
   y = -1

Substitute back to find x:

-5x + 4y = 5
5x + 4(-1) = 5
5x - 4 = 5
5x = 9
x = 1.8

Finally, substitute back to check your work:

5x + 2y = 7  =>  5(1.8) + 2(-1) = 7  =>  9 - 2 = 7  <--True
-5x + 4y = 5  =>  -5(1.8) + 4(-1) = 5  =>  -9 - 4 = 5  <--False

There is no solution.