The greater of two numbers is 1 less than 4 times the lesser. three times the lesser number is 4 less than the greater. find the numbers

So for this, we will be doing a system of equations. Using the info from our question, our two equations are:

(let x = greater number and y = lesser number)

Now, for this I will be using the substitution method. Since we know that x = 4y - 1, substitute that into the second equation:

From here we can solve for y. Firstly, combine like terms:

Next, subtract 4y on both sides of the equation:

Next, multiply both sides by -1:

Now that we know the value of y, substitute it into either equation to solve for x:

In short, 5 is the lesser number and 19 is the greater number.