Question

Find all solutions to the system

Answer 1

`x=-3\\y=5\\\\(-3,5)`

Explanation:

Make both equations equal, as following:

`y=y\\x^(2)+12x+32=6x+23`

Add like terms:

`x^(2)+12x+32-6x-23=0\\x^(2)+6x+9=0`

Factor it as following:

`(x+3)^(2)=0`

Then:

`x=-3` (Double root)

Substitute this into the second equation to obtain y:

`y=6(-3)+23\\y=5`

Then the solution is:

`x=-3\\y=5\\\\(-3,5)`