The sum of two integers is 9 and the sum of their squares is 53. Find the integers.

X + y = 9 Subtract x from both sides.

y = 9 - x

x^2 + y^2 = 53

x^2 + (9 - x) ^2 = 53 Remove the brackets.

x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.

2x^2 - 18x + 81 = 53 Subtract 53 from both sides.

2x^2 - 18x + 81 - 53 = 0

2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.

2 (x^2 - 9x + 14) = 0

2 (x - 2) (x - 7) = 0 You could divide by 2 on both sides. But you can also leave it.

x - 2 = 0

x = 2

x - 7 = 0

x = 7

If x = 2 then y = 7

If x = 7 then y = 2