Question

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.

Answer 1

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

Answer:
There is no solution.