Question

How do you solve the system of equations `4x ^ { 2} + 9y ^ { 2} = 72` and `x ^ { 2} - y ^ { 2} = 5`?

Answer 1

See below
`x=+-3`
`y=+-2`

Explanation:

To solve the system of equations `4x^2+9y^2=72 and x^2−y^2=5`, the easiest method is substitution.

I would solve the second equation for `x^2`
`x^2−y^2=5" "rArr" "x^2=y^2+5`

Substitute this into the first equation
`4(y^2+5)+9y^2=72`
`4y^2+20+9y^2=72`
combine to get: `13y^2+20=72`
subtract `20` from both sides: `13y^2+20-20=72-20`
`13y^2=52`
divide both sides by 13: `(13y^2)/13=52/13`
`y^2=4`
`y=+-2`

Substitute into the other equation
`4x^2+9(4)=72`
`4x^2=36" "x^2=9`
`x=+-3`