The sum of two numbers is 36. Their difference is 6. Find the numbers.

Question

_{show all work and determine if elimination or substitution}

Answer 1

Call the numbers x and y. Now set up the two equations exactly as they are described.

 

x + y = 36

x - y = 6

 

Now add the two equations together. Since one has x +y and one has x -y, the y's will cancel and just x will remain.

 

2x = 42

x = 21

 

Now substitute 21 for x in one of the equations and solve for y.

 

21 + y = 36

y = 15

 

So the answer is 21 and 15.

Answer 2

There aren’t any variables to define, so the first step is to write the equations. In this case, due to the question, only two equations are needed.

x+y = 36

x-y = 6

I will use the elimination method because it is already set up (no changes needed).

x+y = 36

x-y = 6.

2x = 42

x=21 y= (plug back into equation) 15