Question

The sum of two numbers is 2. The sum of three times the larger and twice the smaller is 14. Find the numbers.

Answer 1

For this case we have to:

x: Be the variable that represents the largest number

y: Be the variable that represents the smallest number

We propose a system of equations:

`x + y = 2\\3x + 2y = 14`

From the first equation we have to:

`x = 2-y`

Substituting in the second equation:

`3 (2-y) + 2y = 14\\6-3y + 2y = 14\\6-y = 14\\-y = 14-6\\-y = 8\\y = -8`

We look for the value of "x":

`x = 2 - (- 8)\\x = 2 + 8\\x = 10`

Answer:
`x = 10\\y = -8`