The larger of the two is 1 less than 3 times the smaller number . If twice the smaller number is increased by the larger number, the result is 18 more than the larger number. Find both numbers

3 s = L + 1

2 s + L = L + 18

solve the system

To solve this problem, we need to set up a system of equations based on the given information.

Let's assume that the smaller number is represented by 'x' and the larger number is represented by 'y'.

According to the first statement, the larger number is 1 less than 3 times the smaller number:
y = 3x - 1

According to the second statement, if twice the smaller number is increased by the larger number, the result is 18 more than the larger number:
2x + y = y + 18

Now, we can solve this system of equations to find the values of 'x' and 'y'.

First, let's rearrange the second equation:
2x + y - y = 18
2x = 18
x = 9

Substituting the value of 'x' into the first equation:
y = 3(9) - 1
y = 27 - 1
y = 26

So, the smaller number is 9 and the larger number is 26.