SOLUTION: Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s). The difference betwe

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Question 143786: Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s).
The difference between two numbers is 3, and the sum of those two numbers is 21. What are the two numbers?

Answer by marcsam823(57) (Show Source):
You can put this solution on YOUR website!
Let x = the first number
Let y = the second number
Let x + y = 21
Let x - y = 3
I'll show you two strageties for solving this.
1) The first is the method of addition: add the equations together to eliminate a variable.
2) The second is the method of substitution: solve one of the equations in terms of one variable and and plug in or substitute that expression into the other equations.
Having more than one strategy to solve a problem allows for more flexibility in your approach!
Method of addition:
1) Add the two equations together. Note that each of the y terms cancel each other out. Combine like terms:

+
2)
3) Divide both sides by 12
4) Pick one of the given equations and solve for y by substituting your answer for x.
5) Subtract 12 from both sides
6) Check your answers by substituting into the other equation.

This checks out
The solution is:

Method of substitution:
Let x = the first number
Let y = the second number
Let x + y = 21
Let x - y = 3
1) Select one of the equations and solve for one of the variables (Let's solve our second equation for x}}}

Add y to both sides
2) Substitute this expression for x in the other equation

3) Solve for y:
Combine like terms
Subtract 3 from both sides
Divide both sides by 2

4) Substitute this solution for y and solve for x:

5) Check your answers by substituting your into the other equation:

This checks out
The solution is: