Question

How do you solve by substitution/elimination?

`x^(2)+y^(2)=16`

`(x^(2))/(16)+(y^(2))/(9)=1`

Answer 1

`x = +-4`
`y=0`

Explanation:

`x^2+y^2=16`

`x^2/16+y^2/9=1`

there are a few ways to do it but I would find a common denominator of 16 and 9 and get rid of the fractions then use elimination:

since 16 an 9 share no prime factors the LCD is `16*9 = 144`

`144(x^2/16+y^2/9=1)`

`(144x^2)/16+(144y^2)/9=144`

`9x^2+16y^2=144`

now multiply the other equation by `-9`

`-9(x^2+y^2=16)`
`-9x^2-9y^2=-144`

and add the equations together to solve for y:

`9x^2+16y^2=144`
`-9x^2-9y^2=-144`

`7y^2 = 0`

`y=0`

put y back in either original equation to solve for x:

`x^2+y^2=16`

`x^2+0^2=16`

`x = +-sqrt16`

`x = +-4`