Solve the following system of equations

Question

Give the answer as an ordered pair. If infinitely many solutions, then enter x for x and give y as a function of x:

5x-4y=5

-10x+8y=-10

Answer 1

Although James S. gave you a correct answer, it didn't really answer the question. As he mentioned, there are infinitely many solutions. To answer as an ordered pair, take the equation and solve for "y"

5x - 4y = 5

5x = 4y + 5

5x - 5 = 4y

(5/4)x - 5/4 = y

Then group the "(5/4)x - 5/4" with the "x" as an ordered pair:

(x, (5/4)x - 5/4)

Answer 2

Take the second equation anf divide both sides by -2:

5x -4y = 5

Clearly, it's is now the same equation as the first.

y = 1.25 x -5

Because there is really only one equation, for any x there is a corresponding y. So there are infinitely many solutions.

The mathematical term for this situation is coincidental equations: they are the same.