Question

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

Answer 1

Answer:

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

Step-by-step 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 $\fbox{ -5\:\mathrm{and}\: 11 }$.