Question

How do you solve the system `y - 2x = 3`, `x² + y² = 18`?

Answer 1

`(x,y) = (3/5, 4 1/5)`
or
`(x,y)=(-3,-3)`

Explanation:

Given
[1]`color(white)("XXX")y-2x=3`
[2]`color(white)("XXX")x^2+y^2 =18`

Re-writing [1]
[3]`color(white)("XXX")y=2x+3`

Substituting `(2x+3)` from [3] for `y` in [2]
[4]`color(white)("XXX")x^2+(2x+3)^2=18`

Simplifying
[5]`color(white)("XXX")x^2+4x^2+12x+9=18`

[6]`color(white)("XXX")5x^2+12x-9=0`

Factoring
[7]`color(white)("XXX")(5x-3)(x+3)=0`

`rArr x= 3/5` or `x=-3`

case 1: `color(black)(x=3/5)`
Substituting `3/5` for `x` in [3]
`color(white)("XXX")y=2(3/5)+3= 4 1/5`

case 2: `color(black)(x=-3)`
Substituting `(-3)` for `x` in [3]
`color(white)("XXX")y = 2(-3) +3 = -3`