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Question 276018: A system of linear equations in two variables can have _____ solutions
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A system of linear equations in two variables can have _____ solutions
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0 solutions if the lines are parallel
1 solution if the lines intersect at one point
infinite # of solutions is the two lines overlay one another.
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Cheers,
Stan H.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
A system of linear equations in two variables can have one, no, or infinitely many solutions.
Here are the graphs of an example of two lines
which have 1 solution, because the red and green
lines intersect at the point (2,3), which means they
have ONE point (and only one point) in commone.
the solution is  , 
Here are the graphs of an example of two lines
which have no solution, which means they have
NO points in common:
There can be no solution since the two lines run
parallel (have the same slope) and do not intersect.
Here are the graphs of an example of two lines
which have infinitely many solution, which means they
have ALL points in common
There are INFINITELY MANY solutions since the red line
and the green line are the same line and therefore they
have all their points, INFINITELY MANY points, in common.
Edwin
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