Question

The difference of two numbers is 3. their sum is 13. find the numbers. creater the system and solve

Answer 1

Hey there :)

Let us translate the words into mathematics!

The difference of 2 numbers is 3
x - y = 3

The sum of 2 numbers is 13
x + y = 13

(eq. 1) x - y = 3
(eq.2) x + y = 13
eq. 1 + eq.2 ⇒ x - y = 3
                     + x + y = 13   ( -y and +y cancels out )
                       2x = 16
                        $\frac{2x}{2} = \frac{16}{2}$
                       x = 8

We have the value of x, simply substitute it in either of the formulae to find y

x - y = 3 , 8 - y = 3 , 8 - 3 = y , 5 = y
x + y = 13 , 13 - 8 = y , 5 = y

x = 8 , y = 5