The sum of two numbers is 17 and their difference is 7?

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Answer 1 · 2018-03-08T01:46:41

#5,12#

We can represent the first number with #a# and the second number as #b#. What do we know?

Their sum has to be #color(blue)17#
Their difference has to be #color(red)7#
Given this, we can set up a system of equations:

#a+b=color(blue)17#
#a-b=color(red)7#

If we add our two systems, the #b# terms will cancel, and we're left with:

#2a=24#

#=>color(purple)(a=12)#

Our first number is #a#. Now, we plug #12# in for #a# into both equations. We get:

#12+b=17#

#=>b=5#

#12-b=7#

#=>color(purple)(b=5)#

#a# is #12#, and #b# is #5#. These are our two numbers.