Question

How do you solve 3y=11-2x and 3x=y-11?

Answer 1

Doing some linear algebra, you find that x=-2 and y=5

Explanation:

Set up both equations so y (and coefficients) is alone on the left-hand side (LHS). The first one is already done for you:

`3y=11-2x`
`y=11+3x`

Multiply the second equation by 3, and then subtract equation 2 from equation 1:

`(y=11+3x)*3 rArr 3y=33+9x`

`3y=11-2x`
`-`
`ul(3y=33+9x)`
`0=-22-11x`

Solving for x:

`11x=-22 rArr color(red)(x=-2)`

Now, pick either starting equation and plug in x to solve for y:

`y=11+3x rArr y=11+3(-2)`
`y=11-6 rArr color(blue)(y=5)`