SOLUTION: Find the value of x+(x-y)=71 y-(x-y)=5

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Question 1038914: Find the value of
x+(x-y)=71
y-(x-y)=5
Answer by ikleyn(52879) About Me  (Show Source):
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Find the value of
x+(x-y)=71
y-(x-y)=5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You probably want to say "Find the solution of the system". 

x + (x-y) = 71,    (1)
y - (x-y) =  5.    (2)

Add eqns (1) and (2). You will get

x + y = 76.        (1')

Now distract eqn.(2) from the eqn.(1). You will get

3(x - y) = 66.     (2')

Next divide (2') by 3 (both sides). You will get an equivalent system

x + y = 76,        (1'')
x - y = 22.        (2'').

Now add (1'') and (2''). You will get

2x = 98  --->  x = 98%2F2 = 49.

Then from (1'')  y = 76 - x = 76 - 49 = 27.

Answer.  x = 49, y = 27.