Question about System of equations in 2 variables?

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  Can a system consisting of two linear equations have exactly two solutions? can you explain why or why not?

May 25th, 2015

 soution:

All linear equation can be plot onto the Cartesian plane as a line. 

Solution to a system of linear equation exist only at the intersection of all lines. 

There are only two ways this is possible: 
1) All lines intersect at exactly one point. (One solution) 
2) All lines coincides with one another. (Infinite solutions) 

Exactly 2 solution, thus would not be possible.

if

A system of linear equations can only have one solution. 

Consider 2x + 2 = 0 for a moment. Obviously, this only has one solution. Now, let's say that y = 2. So now we would have 2x + y = 0, which could have a myriad of solutions, as long as y = x/2. 

With the introduction of a second linear equation, however, it limits the possibilities of both variables to only one solution. 

I hope this helps your understanding. You can find my e-mail in my profile, and e-mail me, if it doesn't.

May 25th, 2015

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