Find all solutions to the system

Question

asked Sep 1, 2020 50.3k views

1 Answer

Dallas Clark · Answer 1 · 2020-09-07T17:47:34+0000

Answer:

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

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:

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