Solve the following system of equations. If the system cannot be solved, state that it cannot be solved and explain why. 5x-2y=-24 and -4y=-48-10x

Question

Solve the following system of equations. If the system cannot be solved, state that it cannot be solved and explain why. 5x-2y=-24  and -4y=-48-10x

anonymous · Answer

This system has infinitely many solutions.

anonymous · Answer

yes but what are three solutions ?

anonymous · Answer

I know (0,12), (-24/5,0) and then (?,?)

anonymous · Answer

(2,17) works

anonymous · Answer

how did you get that?

anonymous · Answer

I just guessed on that one. But there is some kind of pattern to the solutions.

anonymous · Answer

wait theres a pattern to the solutions?

anonymous · Answer

From (0,12) to (2,17); notice how we increase the x-value by two and the y-value by 5. Hmmm. What happens to be the slope of this equation?

anonymous · Answer

oh yeah the slope is 5/2, thats interesting, never knew you could find a solution that way.

anonymous · Answer

Well. If you think about it. Since both lines are the same, every point that exists on the line will be a solution to the system; integer, or not.