simultaneous equations help needed

Question

I think of two numbers, $x$ and $y$. When I add them together I get $5$ and when I find the difference I get $13$. What numbers did I think of?

I need to know how to write this down in simultaneous equation form

many thanks

Answer 1

Let's call it $x$,$y$.

Sum: $x+y$

Difference: $x-y$

Can you take it from here?

Answer 2

Two Numbers:

$$x,y$$

The Sum is:

$$x+y=5$$

The difference is:

$$x-y=13$$

Now, let's solve these for $x$

$x+y=5$ and $ x-y=13$

$ x=5-y $ and $ x = 13+y$

Since these two equations have $x$ in common,

$$5-y = 13+y$$

Solve for y,

$$-8=2y \\ y=-4$$

Now we can substitute this $y=4$ to one of the equations,

$$x+y=5 \\ x +(-4) = 5 \\ x-4=5 \\ x=9$$

The numbers you thought of is $x=9$ and $y=-4$

Answer 3

Let the two numbers be $a$ and $b$.From the question,we have

$$a+b=5$$ and $$a-b=13$$.

Adding them we get,$$(a+b)+(a-b)=18$$

$$\implies2a=18$$

$$\implies a=9$$

Substituting $a=9$ in the first equation,we have $9+b=5$ or $b=-4$.

So,$a=9,b=-4$ is the solution.