Question

The sum of two numbers is -36. One number is 106 less than the other. Find the numbers.

Answer 1

71 and -35

Explanation:

so with this we can set up a system of equations

x+y=36

and

x-y=106

now we can add these equations together to eliminate y

x+y=36 plus

x-y=106 equals

2x=142

divide both sides by 2

x=71

now we can plug that in

71+y=36

subtract 71 from both sides

y=-35

Answer 2

-71 and

35

Explanation:

Let the numbers be x and y

x + y = -36

x = y - 106

Substitute y - 106 or x in the first equation

We have

x + y = -36

y - 106 + y = -36

y + y - 106 = -36

2y - 106 = -36

Add 106 to both sides to eliminate -106 on the left side

2y - 106 + 106 = -36 + 106

2y = 70

Divide both sides by 2

2y/2 = 70/2

y = 35

Substitute 35 for y in either equation to get x

Using the second equation, we have

x = y - 106

x = 35 - 106

x = -71

The numbers are 35 and -71

Check

x + y = -36

-71 + 35 = -36

-36 = -36