Question

the sum of two numbers is seven. the sum of the squares of the two numbers is twenty nine. find the two numbers

Answer 1

The two numbers are x and y

x + y = 7 (1st sentence)
x^2 + y^2 = 29 (2nd sentence)

two equations two variables... You could solve by graphing, substitution, or elimination method. Which way are you solving them right now?

Answer 2

substitution

Answer 3

so 25^2+4^2=29 ?

Answer 4

opps i meant 5 not 25

Answer 5

lol

Answer 6

x + y = 7 when I solve for x I get
x = 7 - y substitute that into the second equation

(7 - y)^2 + y^2 = 29 foil method the first binomial
(7 - y)(7 - y) + y^2 = 29
49 - 7y - 7y + y^2 + y^2 = 29 Add like terms

2y^2 - 14y + 49 = 29 set it equal to 0
2y^2 - 14y + 20 = 0 factor (take out the 2 first)
2(y^2 - 7y + 10) = 0 factor
2(y - 5)(y - 2) = 0 set each factor = to 0
y - 5 = 0 or y - 2 = 0 solve each equation
y = 5 or y = 2

if y = 5 then x = 2 because x + y = 7
if x = 5 then y = 2 because x + y = 7

so the two numbers are 2 and 5

Answer 7

yes thanks again