How do solve the following linear system?: # -6x+5y=1 , 7x+2y=2 #?

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Answer 1 · 2018-02-21T00:30:29

By substitution.
#x = 8/47#, #y = 19/47#

#-6x+5y = 1#
#+7x+2y = 2#

We can take out x of the first equation, for example ;

#x = (5y-1)/6#

and we substitute it into the second equation and make all denominators equal :

#7((5y-1)/6) + 2y =2#

#(35y-7)/6 + (12y)/6 = 12/6#

Multiply both sides by #6#.

#35y-7 + 12 y = 12#

#47y = 19#

#y = 19/47#

Then we take this value and put it into our equation for #x#.

#x=((95/47) - 1)/6#

#x=(48/47)/6 = cancel(48)/47 * 1/cancel(6) = 8/47#