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:$x = 10\\y = -8$