Question

Find all solutions to the system

Answer 1

Answer:

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

Step-by-step 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:

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