Given that the difference between two numbers is 11, and when twice the greater number is added to 6 times the smaller one
it becomes 38, determine the two numbers.
Let the larger number be denoted as and the smaller number be denoted as . If the difference between the two numbers is 11, then
If twice the greater number plus six times the smaller number is 38, then
This pair of equations can be solved using the substitution method. Rearranging the first equation gives
Substituting this expression for into the second equation gives
Substituting this value of back into the first equation gives
Therefore, the two numbers are 13 and 2.