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.
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!
2 answers
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?
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?
2 answers