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#