Question

Write a system of equations modeling the given conditions.

The difference between two numbers is 5. The sum of the larger number and twice the smaller number is 14. Find the numbers.

Answer 1

Let's call "x" the larger number and "y" the smaller number.

The difference between the numbers is 5 : x - y = 5

The sum of the larger number and twice the smaller number is 14 :

x + 2y = 14


`\left \{ {{x-y = 5} \atop {x+2y=14}} \right.`


`\left \{ {{x=5+y} \atop {x+2y=14}} \right.`

Let's subsitute x in the second equation, it gives :

5 + y + 2 y = 14
5 + 3y = 14
3y = 14 - 5
y = 9/3 = 3

Let's substitute y in the first equation :

x - y = 5
x - 3 = 5
x = 5 + 3 = 8


Hope this helps !

Photon