Question 143786
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:
 {{{x + y = 21}}}
+{{{x - y = 3}}}

2) {{{2x = 24}}}
3) {{{x = 12}}}  Divide both sides by 12

4) {{{12 + y = 21}}} Pick one of the given equations and solve for y by substituting your answer for x.

5) {{{y = 9}}}  Subtract 12 from both sides

6) {{{(12) - (9) = 3}}}  Check your answers by substituting into the other equation.
   
{{{3 = 3}}}

This checks out
The solution is:
{{{x = 12}}} 
{{{y = 9}}}


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}}}

{{{x - y = 3}}}
{{{x = 3 + y}}}  Add y to both sides

2) Substitute this expression for x in the other equation
{{{x + y = 21}}}
{{{(3 + y) + y = 21}}}

3) Solve for y:
{{{3 + 2y = 21}}}  Combine like terms
{{{2y = 18}}}      Subtract 3 from both sides
{{{y = 9}}}        Divide both sides by 2


4) Substitute this solution for y and solve for x:
{{{x + y = 21}}}
{{{x + 9 = 21}}}
{{{x = 12}}}

5) Check your answers by substituting your into the other equation:
{{{x - y = 3}}}
{{{(12) - (9) = 3}}}
{{{3 = 3}}}


This checks out
The solution is:
{{{x = 12}}} 
{{{y = 9}}}