Question

The sum of two positive integers is 12. When the smaller integer is subtracted from five times the larger, the result is 36. Find the two integers.

Answer 1

The smaller integer is 4 and larger integer is 8 .

Explanation:

First we have to form own variables and expression. So we let the smaller integer be x and the larger integer be y. Next using the information given to form expressions :

`x + y = 12 \\ 5y - x = 36`

Lastly, we can solve the simultaneous equation using Elimination :

`x + y = 12 - - - (1)`

`- x + 5y = 36 - - - (2)`

`(1) + (2)`

`x + ( - x) + y + 5y = 12 + 36`

`6y = 48`

`y = 8`

`sub \: y = 8 \: into \: (1)`

`x + 8 = 12`

`x = 4`