Question

How do you solve x² + y² = 20 and x + y = 6?

Answer 1

When `y=2, x=4`

When `y=4,x=2`

Explanation:

`x + y = 6` `"...................Eq1"`

`x^2 + y^2 = 20` `"..............Eq2"`

`"Using the identity":` `color(red)(x^2+y^2=(x+y)^2-2xy`

`x^2+y^2=(x+y)^2-2xy`

Substituting : `x + y = 6 and x^2 + y^2 = 20`

`20=(6)^2-2xy`

`36-2xy=20`

`-2xy=-16`

`xy=8`

`color(blue)(x=8/y`

Substituting `x=8/y` in `"Eq1"`

`8/y + y = 6`

`8+y^2=6y`

`y^2-6y+8=0`

`(y-2)(y-4)=0`

So, `color(darkred)(y=2 or y=4`

When `color(magenta)(y =2`

`x+2=6`

`color(magenta)(x=4`

When `color(darkorange)(y =4`

`x+4=6`

`color(darkorange)(x=2`

~Hope this helps! :)