Question

How do you solve `8y-1=x, 3x=2y`?

Answer 1

I found: `x=1/11 and y=3/22`

Explanation:

We can trysubstituting the first equation, for `x`, intothe second to get:
`3*(color(red)(8y-1))=2y`
Solve for `y`:
`24y-3=2y`
`22y=3`
So: `y=3/22`
Using this value back into the first equation:
`8*(3/22)-1=x`
`x=(24-22)/22=2/22=1/11`

Answer 2

`(x,y)=(1/11,3/22)`

Explanation:

We have two equations:

`8y-1=x`
`3x=2y`

We can substitute in the value of x (in terms of y) from the first equation into the second, and then solve for y. Like this:

`3(8y-1)=2y`

`24y-3=2y`

`22y=3`

`y=3/22`

And then we substitute into either of the initial equations (I'll do both to show we'll get the same answer for x):

`8y-1=x`

`8(3/22)-1(1)=x`

`24/22-1(22/22)=x`

`24/22-22/22=2/22=1/11=x`

or:

`3x=2y`

`3x=2(3/22)`

`3x=3/11`

`x=1/11`