Question

Which pair of integers has sum equal to -5 ?
-9 and 15
14 and -9
-20 and 15
5 and -5​

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Logan M. asked • 09/19/14

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

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

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Damazo T. answered • 09/19/14

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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