Question

2x-8y=5, -6x+24y=15. I do not think there is any one solution but I'm not sure how to explain why that is.

Answer 1

There is no solution to this set of two equations.
If you multiply the first equation by -3 you get:
-6x + 24y = -15 But the second equation is:
-6x + 24y = 15
Therefore these two equations are inconsistent. There are NO solutions.

Answer 2

NO x,y values can make -6x + 24y both -15 and +15.

Answer 3

Okay that was what I got. So my explanation should be able to be as simple as showing my work and posting that no values make the equations equal?

Answer 4

Yes. There is no pair of (x,y) values that can make -6x + 24y to be -15 to satisfy the first equation and then also make -6x + 24y to be +15 to satisfy the second equation.

Another way to state the same thing is: If you plot the two lines, they will be parallel and they will never intersect. Therefore there will be no intersection point (or solution) that will be on both lines.

Answer 5

Okay awesome. Thank you so much!

Answer 6

you are welcome.