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?

Question

15270 views around the world

You can reuse this answer
Creative Commons License

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#