# If the difference of two numbers is 43 and the sum of the numbers is 13, what are the numbers?

numbers are $28 , - 15$

#### Explanation:

Let $x$ & $y$ be the numbers then

Condition 1:

\text{difference of numbers x& y }=43

$x - y = 43 \setminus \ldots \ldots \ldots . \left(1\right)$

Condition 2:

\text{sum of numbers x& y }=13

$x + y = 13 \setminus \ldots \ldots \ldots . \left(2\right)$

Adding (1) & (2) we get

$x - y + x + y = 43 + 13$

$2 x = 56$

$x = \frac{56}{2}$

$x = 28$

setting the value of $x$ in (1), we get

$28 - y = 43$

$y = 28 - 43$

$y = - 15$

hence the **numbers are $28 , - 15$