Question

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?

Answer 1

nope

Answer 2

I just see at the 2 functions and imagine their graphs, first one is the function of x = 4y move to the left 1 unit, second is the same but move to the right 1 unit, how can they have the same solution?

Answer 3

the only have the same values for x=1 and for y=+-\[\frac{ 1 }{ 4 }\] the values are negative and positive

Answer 4

Notice they look exactly the same one side with just an \(x\). Now since both equal \(x\), it makes sense by the *transitive* property that they also equal one another:$$4y+1=4y-1$$Subtract \(4y\) from both sides and we have:$$1=-1$$OOPS! That's never true! Which means that our equations cannot both be true at the same time; taking a more visual, geometric approach, both equations describe *lines* with the same slope but different \(y\)-intercepts:
Since they have the same slope they have the same direction, but the different intercepts means they're *parallel* and never touch. Solutions would look like intersections between our lines, but since our lines never touch, there are *no* solutions.