The sum of two numbers is 62, and their difference is 8. What are the numbers?

Question

 Solving systems of linear equations by graphing 

Answer 1

27 and 35.

 

I take the sum of 62 and divide by 2 arriving at 31.

 

Next I take the difference 8 and divide by 2 arriving at 4.

 

I now minus 4 from 31 and arrive at one of the solutions 27.

 

Next I add 4 to 31 and arrive at the other solution 35.

 

You could and of course create an algebraic equation but this is an easy trick to apply when there are two solutions.

Answer 2

Let x = the first number

Let y = the second number

 

Using these variables we can write equations.  These equations will be used for graphing.

 

x + y = 62             eq1

x - y = 8                eq2

 

 

To graph these equations, we need to get them in   y=mx+b   form.

 

y = -x + 62              eq1

 

-y = -x + 8    

 

y = x - 8                  eq2

 

 

 

For the first equation:

 

Plot the points (0, 62) and (1, 61) on a coordinate system.  Then connect these points throughout the coordinate system.

 

 

For the second equation:

 

Plot the points (0, -8) and (1, -7) on the same coordinate system.  Then connect these points throughout the coordinate system. 

 

 

You will end up with 2 straight lines.  Find the point of intersection.  That point of intersection is the solution and are the two numbers.