Question

Solve:

3y-x=-2
xy=1

Answer 1

From the second equation, x = 1/y
Sub that into the first equation to solve for y:

3y - 1/y = -2
3y^2 - 1 = -2y
3y^2 + 2y - 1 = 0
(3y - 1)(y + 1) = 0
y = 1/3, -1

Then plug each of those values into either of the original equations to find the corresponding value of x. I'll use the second just because we already solved for x so it's easy:

x = 1/(1/3) = 3
x = 1/(-1) = -1

Answer 2

Thanks I was having the problem cause I was attempting to sub x=3y+2 in to the second equation and it wasn't working.

Answer 3

still unsure why it didn't work.

Answer 4

That would work too. Just easier to isolate either variable in the second equation. But if we do it the other way:

x = 3y + 2
(3y + 2)y = 1
3y^2 + 2y = 1
3y^2 + 2y - 1 = 0

You can see we got the same polynomial as above, so everything else is the same.

Answer 5

sick. I think I distributed the y wrong. lol.