The sum of two numbers is 82. Their difference is 24. How do you write a system of equations that describes this situation and solve by elimination to find the two numbers?

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Answer 1 · 2016-09-30T22:58:43

You must form equations that reflect the statement

Let's call the numbers $x$ and $y$ . The statement can be written as follows:

$x+y=82$
$x-y=24$

Now, both equalities are true for both numbers, so we can now add the two equalities to get a third:

$x+y+x-7=82+24$ , and then

$2x=106$ , and so $x=53$

Now replacing $x$ by its value in either equation, say the first, we have:

$53+y=82$ , and so $y=82-53=29$