The sum of two numbers is 69. the larger number is three less than twice the smaller number. find the numbers. show your work.

So, there's two equations we have here. We'll write them down

x + y = 69    (x will be the larger number)
x = 2y-3       (since it is three less than twice the smaller number, which is y)

So, when you look at the functions, we have a value for x. It would be 2y-3. So, we will plug in 2y-3 into x for the first equation. So, it'll turn to

(2y - 3) + y = 69
2y - 3 + y = 69
3y - 3 = 69
3y = 72
y=24

So, we have the value for the smaller number, 24. So, we will plug in 24 for y in the first equation. That means it will now become

x + (24) = 69
x = 45

So, the large number is 45, and the smaller number is 24