Asked by Bella

Find the number of solutions for this system of equations.

3x + 5y = 20
-2x +5y = 20

How can I do this (and for other systems of equations) without taking all day? Thanks!
Answered by Chris S.
In this particular case, the problem tells you that both formulas equal 20. This means that 3x+5y = -2x +5y.

If you put the ys on one side and the xs on the other, the 5ys disappear.

3x + 5y -5y = -2x + 5y -5y

(what you do on one side, has to be done on the other).

That leaves 3x = -2x.

To get rid of the -2x on the right side, you would add 2x to both sides.

This gives

3x + 2x = -2x +2x

which simplifies to

5x = 0


The only number that works for x here is 0.

If you plug zero in for x in either of the original equations, you then get y = 4.

Answered by drwls
Obviously both equations cannot be true unless x = 0. That means, also, that
5y = 20.
One more step and you can get y.

That didn't take all day.

That is the only one solution.

Actually you were not even asked for what x and y are. You were asked how many solutions there are. Each equation is a straight line on a graph, but they have different slopes. At how many points can two such straight lines intersect?
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