Question

The larger of two numbers is 7 more than 5 times the smaller. If the sum of the two numbers is 31, what are the two numbers

Answer 1

Answer: x=27 y=4

Explanation:

Let the larger of two numbers is x and the smaller of two numbers is y

Hence,

`\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\`

Substitute equation (2) into equation (1):

`31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\`

Divide both parts of the equation by 6:

`4=y\\Hence,\\x=31-4\\x=27`