Do the equations *x* = 4*y* + 1 and *x* = 4*y* – 1 have the same solution? How might you explain your answer to someone who has not learned algebra?

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**The equations x=4y+1 and x=4y-1 have no solutions in common.**

Graphically, these are parallel lines and thus have no common points.

Numerically, it is clear that for any given y, 4y+1>4y-1 so the associated x-values cannot be the same.

4y is equal to 4y so if you add one to that number it cannot be equal to the number minus 1.

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