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:
[tex]x + y = 2\\3x + 2y = 14[/tex]
From the first equation we have to:
[tex]x = 2-y[/tex]
Substituting in the second equation:
[tex]3 (2-y) + 2y = 14\\6-3y + 2y = 14\\6-y = 14\\-y = 14-6\\-y = 8\\y = -8[/tex]
We look for the value of "x":
[tex]x = 2 - (- 8)\\x = 2 + 8\\x = 10[/tex]
Answer:[tex]x = 10\\y = -8[/tex]
