Question

How do you solve the system `x - 3y = 3` and `2x + 9y = 11` by substitution?

Answer 1

`[1]color(white)("XXXXX")x-3y = 3`
`[2]color(white)("XXXXX")2x+9y = 11`

Rearrange [1] to get an expression for `x`
`[3]color(white)("XXXXX")x=3+3y`

Substitute the expression for `x` from [3] into [2]
`[4]color(white)("XXXXX")2(3+3y)+9y = 11`

Simplify
`[5]color(white)("XXXXX")6+6y+9y = 11`
`[6]color(white)("XXXXX")15y= 5`
`[7]color(white)("XXXXX")y=1/3`

Substitute the value of `y` from [7] into [1]
`[8]color(white)("XXXXX")x-3(1/3) = 3`

Simplify
`[9]color(white)("XXXXX")x=4`

The solution is `(x,y) = (4,1/3)`