If x+y=30 and x-y=2, Find x and y. i know the answer but lets see how many ppl can answer this. (Level: Novice)Hint: Solve using...

No algebra!

First equation means like:Two people x and y get a sum of 30 dollars.

The second of the equations means x, one of the two persons, gets 2 dollars more than  the person y.

x and y are names of two persons chosen from your equations. Dollar is only for  making a meaningful practical example of your equatios.

Solution:Keep the 2 dollars, that x should get more than y, separate. The rest of the 30-2=28 dollars, then, have to  be shared equally between x and y : So, 28/2 = 14 that is the value for y.

x should be 2 more than y . So give that 2dollars separated  to x which makes his share : x=14+2=16. This is a commonsense or a method of logic.

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Algebraically you can do by elimination of y from the two given simultaneous equations:

x+y=30      (1)

x-y=2        (2)

There are 2 equalities (or equations). By the postulate that equals can be added to equals and the equality remains we perform the following:

Adding the  given two equations we get 2x=30+2=32.

Therefore,x=32/2=16.

Subtracting  the equation  (2) from (1), we get x  eliminated and only  yor ys  remains on the left:

2y=30-2=28

y=28/2=14.

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Also x +y =30 and x  - y = 2 means that on a number line x is the middle of the stretch  of 2 to 30 and so, x = 16, is the middle. The equidistance on either side of (x=16) is 14 , for  this equal distance from x=16, we get 2 on left and 30 on right. By this interpretation x=16 and y=14 are the solution of these two simultaneous equations. Here is a rough  picture for the imagination only but please do not try measuring it.

line:  |-----y-----------|       |---------y--------| line

(x-y)=2|----------------(x=16)-----------------30=(x+y)

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You can use graph to solve the two equations.

x+y=30 is a many valued equation,representinga straight linecutting x axis at 30 and y axis at 30 units from the origin.

x-y=2 also represents an equation with many solutions, representing a straight line cutting x axis at x=2 and y axis at y=-2.

Both straight lines you can plot and they are perpendicular to each other intersecting at x=16 and y=14 which is the common (or simutaneous unique solution for both equations)

Please plot the following and see where the two graphs cut.

x+y=30 or y= x-30

x=00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30

y=30 28 26 24 22 20 18 16 14 12 10 08 06 04 02 00

x-y=2 or y=x-22:

x=+00 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30

y=-02 00 02 04 06 08 10 12 14 16 18 20 22 24 26 28

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By trial and error way we can come around the solution.

Choose any two numbers such that their sum is 30. Say 10 and 20.The difference gap is 10. Then try reducing their gap by inreasing the smaller. You  increase the smaller ,10 by one , i.e 10+1 =11 and decrease 20 by one , i.e to 19. Now the  gap is reduced from 10 to 9. Inrease by one by one the lower number and decrease the greater number one by one  till their difference  of two  resulting number become 2. The number finally is 14 and 16. 16 is ,therefore, x and cosequently, 14 is y

Hope this helps.