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The system x + y =1          has an infinite number of
solutions, including (0,1) (1,0) and (2, -1). Explain why.
                 2x + 2Y = 2

The system y = 2x +1      has no solution.  (That is to say, there is no
ordered pair that satisfies both equations of the system)
                  y = 2x =3        Explain why.

The system x+y=1 and 2x+2y=2 have an infinite number of solutions because, on a graph, they are the same line. They touch at an infinite number of points. The equations y=2x+1 and y=2x+3 are parallel lines on a graph. They do not touch at any point. The solution to a system of equations is a point that is shared by both graphs. The first system shares an infinite number of points. The second system shares none.

Kenneth Mellendorf

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