Algebra, impossible answer?

Question

I did a math test yesterday. There was one question that said:

8x - y = 10

and I was supposed to find a way that x and y could have the same value.

I did an equation like this:

8x - y = 10

8x = 10 + y

8 = (10+y) / x

10 / 8 = y / x

but since y and x are supposed to have the same value, 10 / 8 would be equal to 1 which isn't true of course.

So I answered that there was no answer, suspecting it was a trick question.

My question is this: Did I do the equation correctly, and is there truly no value that both x and y could share?

Answer 1

Nice try

8x - y = 10

8x - x = 10 <--- fixed point: substitutes y=x

7x = 10

x = 10/7 <--- so 10/7 is the fixed point

CHECK

for =10/7

8(10/7) - y = 10

80/7 - y = 10

80 - 7y = 70

10 - 7y = 0

10 = 7y

y = 10/7

The fixed point is x=y=10/7