There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers.

Let the first number be x and the second number be y. We have 2 equations:

1. 4x + 3y = 24
2. 2x - 3y = 24

Without doing anything else, we can add the 2 equations together to eliminate the y term:
(4x + 2x) + (3y - 3y) = (24 + 24)
6x = 48

Divide each side by 6:
x = 8

Substitute this into equation (1)
4(8) + 3y = 24
32 + 3y = 24

Type 32 + 3y = 24 into our search engine and we get y = 2.6667.