Find the value of x and y if there sum is 8 and 13

Question

Find the value of x and y if the sun of numbers is 13, 8 and difference is 6

Answer 1

Let’s ignore the actual sum and difference values and use the letters S for sum and D for difference:

Assuming x>y, x+y=S and x-y=D. So adding these equations we get:

2x=S+D, making x=½(S+D). Now subtract the second equation from the first:

2y=S-D, making y=½(S-D).

So x is half the sum of the sum and difference of x and y; and y is hafl the difference of the sum and difference of x and y.

The question gives us three numbers: 8, 13 and 6. We need only two numbers to find x and y. The only numbers for sum and difference that give us whole numbers for x and y are the even numbers 8 and 6. If S=8 and D=6, x=7 and y=1. Note that, if S=6 and D=8, x=7 and y=-1.

If 13 is the sum, and 6 the difference, S=13 and D=6, making x=19/2 and y=7/2.

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