Answer: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
