Twice one number plus a second number is 42, and the first number minus the second number is -6. Find the numbers

Question

Work problem in my math homework 

Answer 1

Hi Evette,

 

First, pick variables to represent the unknowns.

Let x = first number

Let y = second number

 

Twice one number plus a second number is 42:

2x + y = 42

first number minus the second number is -6:

x - y = -6

 

If we add the two equations the y variable is eliminated

and we can solve for x.

 

2x + y = 42

x - y = -6

----------------

3x = 36

 

x = 36/3

 

x = 12

 

Using that and the fact that x - y = -6 we can find y

12 - y = -6

-y = -18

y = 18

 

Your numbers are 12 and 18

 

Check:  2x + y = 42

            2(12) + 18 = 42

            24 + 18 = 42

            42 = 42

 

            x - y = -6

            12 - 18 = -6

            -6 = -6