The sum of two numbers is 14 and the diference is 6 what are the two numbers?

2 Answers
Mar 11, 2018

#a = 10 and b = 4#.

Explanation:

Let a be the larger and b be the smaller. We know that

#a+b = 14 and a-b = 6#.

Solving the 2nd equation for a,

#a = 6 + b#.

Substituting that expression for a in for the a in the first equation, and then solving for b,

#6+b+b = 14#

#2*b = 14-6 = 8#

#b = 8/2 = 4#
Therefore #a = 6+4 = 10#.

I hope this helps,
Steve

Mar 11, 2018

#10# and #4#.

Explanation:

Let's call the two numbers #x# and #y#. We know that #x+y=14# and #x-y=6#. We could guess and check, but there is an easier way. We can use elimination to solve for #x# and #y#, using *just these two equations! *


Why?
We can rewrite these two equations as #1x+1y=14# and #1x+(-1y)=6#. Note that #x#'s coefficients are the same, so we can subtract the equations and #x# will disappear, leaving us with the solution for #y#. Also note that #y#'s coefficients are additive inverses, so we can add the equations and #y# will disappear, giving us the solution for #x#! That's both variables! Here we go:


Subtracting (solution for #y#):
#cancel(x)+y=14#
#cancel(x)-y=6#
#y-(-y)=8 #y+y=8# #2y=8# #y=4# **So, one of the numbers is #4#.**

Adding (solution for #x#)
#xcancel(+y)=14#
#xcancel(-y)=6#
#2x=20#
#x=10#
So, the other number is #10#.


Let's check:
#x+y=14#
#10+4=14#
#14=14#


#x-y=6#
#10-4=6#
#6=6#
We're good!

So, the two numbers are #10# and #4#.