Do the equations x = 4y + 1 and x = 4y – 1 have the

same solution? How might you explain your answer to someone who has not learned

algebra? How do you solve? This is for new learners in Algebra.

There is no common solution to these two equations. There are a number of ways to explain why.

One way is to notice that the left hand sides of both equations are equal (both are just x).

Therefore the right hand sides must be equal. But then you have 4y + 1 = 4y - 1. Cancelling the 4y on both sides gives 1 = -1 which is clearly false.

Another way to see it is that the lines have the same slope but different intercepts and are therefore parallel. Two parallel lines never intersect so there is no common solution.