Question

What are the two numbers and how did you figure it out?

Answer 1

I would make a list of the factors of 12. 1 and 12; 2 and 6; 3 and 4. However none of these add to 10. I would talk to a teacher about this one, since none of the answers are apparent at the moment. I will keep working.

Answer 2

do those 2 equaiton you did
minus x on top

y=10-x
sub for y
x(10-x)=12
distribute
10x-x^2=12
minus (10x-x^2) both sides
0=x^2-10x+12

use quadratic formula
in form
ax^2+bx+c=0
x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`

a=1
b=-10
c=12
x=
`\frac{-(-10)+/- \sqrt{(-10)^(2)-4(1)(12)} }{2(1)}`
x=
`(10+/- √(100-48) )/(2)`
x=
`(10+/- √(52) )/(2)`
x=
`(10+/- 2√(13) )/(2)`
x=
`5+/- √(13)`


x=
`(5+ 2√(13) )/(2)` or
`(5- 2√(13) )/(2)`

aprox

x=1.39445 or 8.60555
those are the 2 numbers since x and y can switch