SOLUTION: The sum of two number is ten while the sum of their square is fifty-eight. What are the numbers?

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Question 480114: The sum of two number is ten while the sum of their square is fifty-eight. What are the numbers?
Answer by Maths68(1474) About Me  (Show Source):
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x+y=10
x=10-y..........(1)
x^2+y^2=58......(2)
Put the value of x in equation (2)
(10-y)^2+Y^2=58
100-20y+y^2+y^2=58
100-20y+2y^2=58
Divide by 2 both sides of the equation
50-10y+y^2=29
y^2-10y+50-29=0
Y^2-10y+21=0
y^2-7y-3y+21=0
y(y-7)-3(y-7)=0
(y-7)(y-3)=0
y-7=0 or y-3=0
y=7 or y=3
Put the values of y in equation (1)
when y=7
x=10-7
x=3
When y=3
x=10-3
x=7
So two numbers are 7,3