SOLUTION: 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?

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Question 689901: 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 by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+4y+%2B+1 and
x+=+4y+%96+1
if you assign a number to x and solve both equation for +y you will need to get same value for +y IF they have same solution
let's check it:
let's x=0
0+=+4y+%2B+1 ...solve for y
-1+=+4y+
highlight%28-1%2F4+=+y%29+
and
0+=+4y+%96+1
1+=+4y
highlight%281%2F4+=+y%29
since highlight-1%2F4%3C%3E1%2F4++, the two equations do not have the same solution; it means these lines are parallel and do not intersect
check it on a graph
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4y+%2B+1%2C+4y+-1%29+

you also can come to same conclusion this way:
first write both of them in slope-intercept form y=mx%2Bb like this:
x+=+4y+%2B+1..=>..x-1+=+4y.=>..%281%2F4%29x-1%2F4+=y. or y=%281%2F4%29x-1%2F4+
and
x+=+4y+-1..=>..x%2B1+=+4y.=>..%281%2F4%29x%2B1%2F4+=y. or y=%281%2F4%29x%2B1%2F4+
as you can see both lines have same slope m=1%2F4 and, by definition, the lines with same slope are parallel
if the lines parallel, they have no intersection point, and they have no same solution