Question

Twice a number minus a second number is -1. Twice the second number added to three times the first number is 9. How do you find the two numbers?

Answer 1

The first number is `1` and the second number is `3`.

Explanation:

We consider the first number as `x` and the second as `y`. From the data, we can write two equations:

`2x-y=-1`
`3x+2y=9`

From the first equation, we derive a value for `y`.

`2x-y=-1`

Add `y` to both sides.

`2x=-1+y`

Add `1` to both sides.

`2x+1=y` or `y=2x+1`

In the second equation, substitute `y` with `color(red)((2x+1))`.

`3x+2color(red)((2x+1))=9`

Open the brackets and simplify.

`3x+4x+2=9`

`7x+2=9`

Subtract `2` from both sides.

`7x=7`

Divide both sides by `7`.

`x=1`

In the first equation, substitute `x` with `color(red)1`.

`(2xxcolor(red)1)-y=-1`

`2-y=-1`

Add `y` to both sides.

`2=y-1`

Add `1` to both sides.

`3=y` or `y=3`