Question 922633
These kind of problems are done the same way.
let a & b be the two numbers. Write an equation for each statement
:
"The sum of two numbers is eleven."
a + b = 11
b = (-a+11); use this form for substitution
: 
"The sum of the squares of the two numbers is eighty-five."
a^2 + b^2 = 85
replace b with (-a+11)
a^2 + (-a+11)^2 = 85
FOIL (-a+11)(-a+11)
a^2 + a^2 - 11a - 11a + 121 = 85
combine like terms
2a^2 - 22a + 121 - 85 = 0
a quadratic equation, we can solve
2a^2 - 22a + 36 = 0
simplify, divide by 2
a^2 - 11a + 18 = 0
Factors to
(a-2)(a-9) = 0
two solutions
a = 2, then b = 9
a = 9, then b = 2
" Find the two numbers." 2 & 9
:
Did you find you could follow what we did here?