# The Sum Of Two Numbers Is 11 And Their Difference Is 6. Can You Find The Numbers?

Sum of two numbers is 20 difference is 4
thanked the writer.
Step 1:  Establish variables for your numbers.  I am going to call them X and Y

Step 2:  Establish the information you are given

Given X + Y = 11 (the sum of the numbers is 11) ... Equation 1
Given X - Y = 6 (their difference is 6)  .... Equation 2

Step 4: Using one of the equations, get one variable in terms of everything else.

I will use equation 1, and get X in terms of everything else.

X + Y = 11
X + Y - Y = 11 - Y ..... Subtract Y from both sides

X = 11 - Y

Using this information substitute it into equation 2

X - Y = 6 .... Equation 2

(11 - Y) - Y = 6 .... Substitute 11 - Y for the variable X

11 - Y - Y = 6
11 - 6 - 2y = 6 - 6 .... Subtract 6 from both sides
5 - 2Y = 0
5 - 2Y + 2Y = 0 + 2Y .... Add 2Y to both sides

5 = 2Y
2.5 = Y ... Divide both sides by 2

We now have a value for Y. Y = 2.5

We also know that X - Y = 6
So lets substitute 2.5 into this equation for Y

X - 2.5 = 6

X = 6+2.5

X = 8.5

Now always do a check

Y = 2.5, X = 8.5

What is the sum of X + Y , 2.5 + 8.5 = 11 ... This is correct (we were told this)
What is the difference between the two 8.5 - 2.5 = 6 ... This is correct (we were told this)

I hope this helps.
thanked the writer.
Let the numbers are x and y
then, x+y = 11...(1)

x-y = 6....(2) 