The difference of two numbers is 3. their sum is 13. find the numbers

The two numbers are 8 and 5.

Consider the two numbers as x and y. From the given data, we write:

x−y=3
x+y=13

From the first equation, we determine a value for x.

x−y=3

Add y to both sides.

x=y+3

In the second equation, substitute x with (y+3).

x+y=13

(y+3)+y=13

Open the brackets and simplify.

y+3+y=13

2y+3=13

Subtract 3 from each side.

2y=10

Divide both sides by 2.

y=5

In the first equation, substitute y with 5.

x−y=3

x−5=3

Add 5 to each side.

x=8

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