Question

The sum of two numbers is -6. The difference is 16. Find the two numbers.

Answer 1

`-5\:\mathrm{and}\: 11`

Explanation:

We can write the following system of equations:

`\begin{cases}x+y=6\\x-y=16\\\end{cases}`

Adding both equations together, we isolate
`x` and get:

`2x=22,\: x=11`

Plugging
`x=11` in any of the equations, we can solve for
`y`:

`11+y=6,\: y=-5`

Verify that the solution pair
`(11, -5)` works
`\checkmark`

Therefore, the two numbers are
`\fbox{$-5\:\mathrm{and}\: 11$}`.