Given:
a.) The sum of two integers is 20.
b.) Three times one integer is 3 less than 6 times the other integer.
Let,
x and y represents the two integers
x + y = 20
3x = 6y - 3
Let's determine using the Substitution Method:
x + y = 20
y = 20 - x
Substitute y = 20 - x in 3x = 6y - 3. We get,
3x = 6y - 3
3x = 6(20 - x) - 3
3x = 120 - 6x - 3
3x + 6x = 120 - 3
9x = 117
9x/9 = 117/9
x = 13
Let's determine the other integer, substitute x = 13 in x + y = 20 to find y.
x + y = 20
13 + y = 20
y = 20 - 13
y = 7
Therefore, the two integers are 13 and 7. Both are positive integers.