The sum of the digits of a two digit number is 7, and their product is 10. what is the number?
100pts

The numbers are 5 and 2

Step-by-step explanation:

Let x represent the first digit number.

Let y represent the second digit number.

The sum of the digits of a two digit number is 7. This means that

x + y = 7 - - - - - - - - - - - -1

The product of the digits is 10. This means that

xy = 10 - - - - - - - - - - - -2

Substituting x = 7 - y into equation 2, it becomes

y(7 - y) = 10

7y - y^2 = 10

y^2 - 7y + 10 = 0

y^2 - 5y - 2y + 10 = 0

y(y - 5) - 2(y - 5) = 0

y - 2 = 0 or y - 5 = 0

y = 2 or y = 5

Substituting y = 2 or y = 5 into

x = 7 - y, it becomes

x = 7 - 2 = 5 or x = 7 - 5 = 2

The numbers are 5 and 2