The sum of two numbers is 21, and their difference is 9

The numbers are 15 and 6.

Step-by-step explanation:

We can solve the problem algebraically (using equations). First, write equations that represent the situation.

Choose variables to represent the numbers:

let the numbers be "x" and "y"

Take apart each section of the problem and make an equation.

"The sum of two numbers is 21"

x + y = 21 Sum means the answer when you add numbers

"Their difference is 9"

x - y = 9 Difference means the answer when you subtract numbers

Using the two equations, you can solve using elimination. With this method, you get rid of one of the variables, so you can easily solve for the other one. You can use elimination when one of your variables have the same variable number. Both equations have "1x" and "1y" ("1" is never written).

Add the equations together by adding normally, with each of the terms with the same variable.

. x + y = 21 Add each term

+ x - y = 9 (x + x = 2x) (y + (-y) = 0) (21 + 9 = 30)

. 2x + 0 = 30 "y" variable cancelled out

. 2x = 30

. 2x/2 = 30/2 Divide both sides by "2" to isolate "x"

. x = 15 Answer for one number

To find the other number, substitute 'x' for 15 into one of the equations.

x + y = 21

15 + y = 21 Isolate "y" now

15 - 15 + y = 21 - 15 Subtract 15 from both sides

y = 21 - 15 15-15 cancelled out on the left side. Solve right side.

y = 6 Answer for second number

Therefore the two numbers are 15 and 6.

let's say the two numbers are x and x + 9. so we know x + x + 9 = 21, so 2x + 9 = 21. subtract 9 from both dies to get 12 = 2x. divide both sides by 2 to get x = 6. so your two numbers are 6 and 15.