How do you solve the system of equations algebraically #3/5x-1/6y=1, 1/5x+5/6y=11#?

1 Answer
Aug 12, 2017

Answer:

#y=12,x=5#

Explanation:

#3/5 x-1/6 y=1#------(1)

#1/5 x+5/6 y=11#------(2)

#:.(1) xx 5#

#:.(5)3/5x-(5)1/6y=5#

#:.15/5x-5/6y=5#

#:.3x-5/6 y=5#------(3)

#:.(2)+(3)#

#:.3 1/5x=16#

#:.16/5 x=16#

#:.x=16/(16/5)#

#:.x=cancel(16)^1/1 xx 5/cancel(16)^1#

#:.color(magenta)(x=5#

substitute #color(magenta)(x=5# in(1)

#:.3/5(color(magenta)5)-1/6 y=1#

#:.15/5-1/6y=1#

#:.3-1/6 y=1#

#:.-1/6 y=1-3#

#:.-1/6 y=-2#

#:.y=2/(1/6)#

#:.y=2 xx 6#

#:.color(magenta)(y=12#

substitute #color(magenta)(y=12,x=5# in (2)

#:.1/5(color(magenta)5)+5/6(color(magenta)12)=11#

#:.5/5+60/6=11#

#:.1+10=11#

#:.color(magenta)(11=11#