Question

the sum of two numbers is 82. their difference is 24. write a system of equations that describes this situation. solve by elimination to find the two numbers. a. x y = 82 x – y = 24 53 and 29 b. x y = 82 x – y = 24 48 and 24 c. x y = 24 y – x = 82 48 and 30 d. x – y = 82 x y = 24 52 and 30

Answer 1

Let the two numbers be x and y.

x + y = 82
+ Add both equations
x - y = 24
________

2x = 106
_________

x = 106/2

x = 53


Recall: x + y = 82 53 + y = 82 , y = 82 - 53 = 29

Therefore x = 53, y = 29

Answer 2

The value of x and y is 53 and 29 respectively.

Explanation:

Consider the provided information.

Let the two numbers are x and y.

The sum of two numbers is 82.

`x+y=82`

Their difference is 24.

`x-y=24`

Now solve the equation by elimination method.

`x+y=82\\\underline{x-y=24}\\2x\ \ \ \ =106`

`x =53`

Now, substitute the value of x in
`x+y=82`.

`53+y=82`

`y=82-53`

`y=29`

Hence, the value of x and y is 53 and 29 respectively.