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 = 24 y – x = 82 48 and 30

c. x – y = 82 x + y = 24 52 and 30

d. x + y = 82 x – y = 24 48 and 24

Let the 2 numbers be x and y.

Sum of the two numbers is 82.

x + y = 82 ---(1)

Difference of the two numbers is 24.

Add equations (1) and (2)

x + y + x - y = 82 + 24

2x = 106

x = 106/2

x = 53

Substitute value of x in equation (2)

53 - y = 24

y = 53 - 24

y = 29

So, the 2 numbers are 53 and 29.

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