How to solve this math problem

solve for x and y if

2x+y=12
xy=16

2x+y=12, so y=12-2x

Substituting into the other equation:

x(12-2x)=16

12x-2x^2=16

2x^2-12x+16=0

x^2-6x+8=0

(x-2)(x-4)=0

x=2 or x=4

To get y, you know that y=12-2x, so:
y=12 - 2(2) or 12 - 2(4)
= 8 or 4

So the two possible solutions are x=2 and y=8, or x=4 and y=4

2x + y = 12
y = 12 - 2x

xy = 16
x(12 - 2x) = 16
12x - 2x^2 = 16
0 = 2x^2 - 12x + 16
0 = 2(x^2 - 6x + 8)
0 = 2(x - 4)(x - 2)

x = {2, 4}
y = {8, 4}

(2, 8) and (4, 4)

x=4
y=4