Question

Describe the possible solution sets for a system of two linear equations, and explain why these are the only possibilities.

Answer 1

The graphical representation of a system of two linear equations is two lines. These two lines can
(1) interesct at a point (x, y)
(2) not intersect and be parallel (no solution)
(3) sometimes turn out to be the same line (infinitely many solutions).

These are the only possibilities for a system of two linear equations because when graphed, they will only do these three things.

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