Question

How many solutions are there to the following system of equations?



2x – y = 2
–x + 5y = 3

A.
2


B.
0


C.
1


D.
infinitely many

Answer 1

we are going to put these in y = mx + b form and compare the slopes and the y intercepts. In y = mx + b form, the slope is in the m position and the y int is in the b position.

2x - y = 2
-y = -2x + 2
y = 2x - 2
the slope is 2 and the y intercept is -2

-x + 5y = 3
5y = x + 3
y = 1/5x + 3/5
the slope is 1/5 and the y intercept is 3/5

Compare : the slopes are different and the y intercepts are different. This means that the line will intersect in 1 place. There is 1 solution.
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Learn this :
If the slopes are the same, but the y intercepts are different....this means the lines are parallel and have no solution.

If the slopes are the same and the y intercepts are the same...this means that the lines coincide and have infinite solutions.

if the slopes are different and the y intercepts are different...this means they will intersect giving you 1 solution