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

They have no solution.

You are given two parallel lines, which of course cannot meet

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To determine if the equations x = 4y + 1 and x = 4y - 1 have the same solution, we need to compare the two equations and see if they yield the same values for x and y.

Let's start by solving the two equations simultaneously. We can do this by setting the expressions for x in both equations equal to each other:

4y + 1 = 4y - 1

Now we can solve for y:

Subtracting 4y from both sides, we get:

1 = -1

As we can see, the equation 1 = -1 is not true. This means that the equations x = 4y + 1 and x = 4y - 1 do not have the same solution.

In conclusion, the two equations do not have the same solution because the equation derived from solving them simultaneously is not true.