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.