Two integers have a difference of 6 and a sum of -18. What are the two integers?

Question

Two integers have a difference of 6 and a sum of -18. What are the two integers?

Answer 1

Let x be the smaller integer

Let y be the larger integer

 

Their difference is -6. Difference implies subtraction. So, x-y=6

Their sum is -18. Sum means addition. Thus, x+y= -18

 

so, we have what is called a System of Linear Equations. There are many different ways to solve a system of linear equations. You can use the Elimination Method, the Substitution Method, graph them, use matrices. 

 

I am going to use the Elimination Method. We have:

 

x - y = 6

x + y = -18

 

add the top equation to the bottom equation.

 

x+ x= 2x   ,  (-y)+y= 0   and. 6 + (-18)= -12

 

So,  2x= -12

       x= -6

To find y, plug in -6 for x in either x-y=6 or x+y= -18.  I am going to choose the latter, x+y= -18.  Substituting -6 for x, we have:

 

(-6)+y = -18

+6.          +6   Adding six to both sides

0     + y = (-12)

 

final answer :  y= -12 ,  x= -6

Answer 2

Let x = the larger integer      and let y = the smaller integer

 

 x - y = 6

x + y = -18

2x     = -12

      x = -6

 

  x + y = -18

-6 + y = -18

       y = -12