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