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Parallel Lines Have How Many Solutions To Systems Of Linear Equations

A solution to a system of linear equations is the place where the two lines, if you graph them, cross.

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Parallel lines do not ever cross. So there”s zero solutions.

However!! There”s a tiny, tiny chance this could be a trick question. Because often, the equation of two lines that look parallel are actually the same line, in which case the system will produce an infinite number of solutions.

The way to be sure is just to pick an x value completely at random, put it into both equations, and see if the answers are equal. If it”s really two parallel lines, they won”t be. If they”re secretly the same line and the whole thing is a trap, then they will, as will any random number you come up with to put in for x.

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