## vegas14 4 years ago Create your own two-step equation with NO SOLUTION as the solution. Show the steps to solving the equation and explain in words why your work proves that there are NO SOLUTIONS

1. agreene

by two step do you mean that it only has two operations?

2. vegas14

yes

3. agreene

well, the easiest way to think about this is to think of something that is undefined... 0/0 comes to my mind. So then you have to either add that to an equation or represent it as the equation. y=x+0/0 has no solutions. But, im not sure if that is exactly what they're asking for.

4. elecengineer

^Thats not what they are asking for. something like 3x+5 = 3x+6 is what they are asking for.

5. elecengineer

If you try to subtract 3x from both sides you get 5=6, which is a contradiction, so there are no solutions.

6. elecengineer

From a geometric point of view the lines are parallel (with one line being the other line , shifted up by one unit). Parallel lines will not interest each other so there is no solution.

7. across

Just for the heck of it, throw a "... in Euclidean space..." somewhere near the end of your answer. Parallel lines intersect (possibly more than once) in certain non-Euclidean spaces. ;P