Answer: the integers are 6 and 23
Explanation:
Let x represent one of the integers.
Let y represent the other integer.
The product of the integers is 138. This means that
xy = 138 - - - - - - - - - -1
One of the integers is seven less than five times the other integer. This means that
x = 5y - 7
Substituting x = 5y - 7 into equation 1, it becomes
y(5y - 7) = 138
5y² - 7y = 138
5y² - 7y - 138 = 0
5y² + 23y - 30y - 138 = 0
y(5y + 23) - 6(5y + 23)
y - 6 = 0 or 5y + 23 = 0
y = 6 or y = - 23/5
The only possible value of y is 6
x = 138/y = 138/6
x = 23