If 7a+3b=20 and 3a+7b=10, then what is the value of a+b?

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Answer 1 · 2017-05-17T03:43:07

#a+b=3#

We first have to solve the simultaneous equations:

#7a+3b=20# [A]
#3a+7b=10# [B]

[A] #-> a=(20-3b)/7# [C}

Replace for #a# in [B]:

#3((20-3b)/7) + 7b =10#

#(60-9b)/7 +7b=10#

Multiply through by 7:

#60-9b +49b=70#

#40b = 10 -> b=1/4 =0.25#

Replace for #b# in [C]:

#a= (20-3xx0.25)/7#

#= (20-0.75)/7 = 2.75#

This questions asks for the sum of #a# and #b#:

#a+b= 0.25+2.75 =3#