Question

Two times a number plus three times another number equals 13.The sum of the two numbers is 7.What are the numbers?

Answer 1

The two numbers are `8` and `-1`

Explanation:

Let `x` and `y` be the numbers:

`2x+3y=13`
`x+y=7=>` `y=7-x`:
`2x+3(7-x)=13`
`2x+21-3x=13`
`x=8`
`y=7-8=-1`

Check:
`2*8+3*(-1)=16-3=13`
`8-1=7`

Answer 2

The numbers are `8` and `-1`

Explanation:

You can solve this by using `2` variables and making two simultaneous equations.

But we know the relationship between the two numbers (they add to `7`) so it is possible to use one variable.

Let one number be `x`. The other number is `7-x`

Write an expression for "Two times one number plus three times the other number:"

`2x + 3(7-x)`

Make an equation: The sum is equal to `13`

`2x + 3(7-x) =13`

`2x+21-3x=13`

`-x = 13-21`

`-x = -8`

`x=8`

If one number is `8`, the other number is `7-8 =-1`

Check:

`2 xx 8 + 3xx(-1)`
`=16-3`
`=13`