Question

Find two numbers, if their sum is −11 and their difference is 41

Answer 1

The larger one is (-11 + 41)/2 = 15.

The smaller one is (-11 -41)/2 = -26.

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For two numbers a and b with sum s and difference d, you can write the equations

$a+b=s\\a-b=d$

Then adding the equations and dividing that sum by 2, you get

$(a+b)+(a-b)=(s)+(d)\\2a=s+d\\a=\dfrac{s+d}{2}$

You can subtract the second eqution from the first and get a similar result for the smaller number

$(a+b)-(a-b)=(s)-(d)\\2b=s-d\\b=\dfrac{s-d}{2}$

These are the formulas we used above.