Question 671826
No, the equations x = 5y + 3 and x = 5y – 3 do NOT have the same solution because this system is inconsistent (and therefore, there are no solutions at all).



A way to explain it to someone who has not learned algebra:


y is some number. So 5 times y (5y) is some (different) number as well.


This means that


x = <font color="red">5y</font> + 3


is the same as 


x = <font color="red">Some Number</font> + 3


and


x = <font color="red">5y</font> - 3


is the same as 


x = <font color="red">Some Number</font> - 3


But we have a problem. x can only be ONE number at a time; however, the statements "some number + 3" and "some number - 3" yield different numbers every time (for any number that replaces "some number"). Go ahead and try it out with a few numbers.


So we get a contradiction which leads to no solutions.