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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

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olemakpadu
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:

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

Step-by-step explanation:

Consider the provided information.

Let the two numbers are x and y.

The sum of two numbers is 82.

[tex]x+y=82[/tex]

Their difference is 24.

[tex]x-y=24[/tex]

Now solve the equation by elimination method.

[tex]x+y=82\\\underline{x-y=24}\\2x\ \ \ \ =106[/tex]

[tex]x =53[/tex]

Now, substitute the value of x in [tex]x+y=82[/tex].

[tex]53+y=82[/tex]

[tex]y=82-53[/tex]

[tex]y=29[/tex]

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