SOLUTION: Suppose you are given the sum and the difference of two real numbers. How can you figure out what the numbers are themselves? Explain your reasoning clearly step by step.

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Question 393707: Suppose you are given the sum and the difference of two real numbers. How can you figure out what the numbers are themselves? Explain your reasoning clearly step by step.
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose you are given the sum of two real numbers
first name these numbers like x and y
the sum of them you will write like x+%2B+y%7D%7D+and+it+will+be+equal+to+certain+number%2C+for+example+%7B%7B%7B10
write an equation:
now write the other equation
x+-+y+=+4....(2)



now you have a system of two equations with two unknown variables
x+%2B+y+=+10....(1)...
x+-+y+=+4....(2)
---------------------------
now take any equation of these two and solve for one variable, for example x
x+%2B+y+=+10....(1)...solve for x
x+=+10+-+y....(1)...now substitute it in second equation
%2810+-+y%29+-+y+=+4....(2)and solve for y
10+-+y+-+y+=+4
10+-+2y++=+4
10+-+4++=+2y
6++=+2y
6%2F2++=+2y%2F2
3+=+y..................now you can find x

x+=+10+-+y=+10+-+3+=+7
so, your numbers are x=7 and y+=+3
check: plug in values for x and y+
x+%2B+y+=+10....(1)...
7+%2B+3+=+10
10+=+10

x+-+y+=+4....(2)
7+-+3+=+4
4+=+4







Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
eg
x - y = a
x + y = b
---------- Add
2x = a+b
x = (a+b)/2
------------
y = x - a or
y = b - x