The sum of two numbers is 82. Their difference is 24. Write a system of equation

Mathematics
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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
      xy = 24
      53 and 29

b.   x + y = 24
     yx = 82
    48 and 30

c.    xy = 82
      x + y = 24
     52 and 30

d.    x + y = 82
       xy = 24
      48 and 24

Apr 29th, 2015

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.

x - y = 24 ---(2)


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.


ANSWER:  

a. x + y = 82
      x – y = 24
      53 and 29

Apr 29th, 2015

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