How do solve the following linear system?: # 2x+6y=5 , x-7y=4 #?

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Answer 1 · 2016-02-09T11:23:16

#x=2 19/20; y=-3/20#

#2x+6y=5 (1) #
# x - 7y=4 (2)# Multiplying Equation (2) by 2 and then subtracting from equation (1) We get
#2x+6y=5 (1) #
#2x-14y=8 (2)#

#20*y=-3# #:. y=-3/20 and x= 4+ 7*(-3/20) =4-21/20=59/20#{Ans]

Answer 2 · 2016-02-09T11:50:41

#x,y=2 19/20,-3/20#

Solve by elimination:

#color(blue)(2x+6y=5),color(green)(x-7y=4)#

We can eliminate #2x# from the first equation by #x# in the second equation by multiplying it with #-2# to get #-2x#.

#rarr-2(x-7y=4)#

#rarr-2x+14y=-8#

Add both the equations:

#rarr(2x+6y=5)+(-2x+14y=-8)#

#rarr20y=-3#

#rarry=-3/20#

Substitute the value to the first equation:

#rarr2x+6(-3/20)=5#

#rarr2x+(-18/20)=5#

#rarr2x+(-9/10)=5#

#rarr2x-9/10=5#

#rarr2x=5+9/10#

#rarr2x=59/10#

#rarrx=59/10-:2#

#rarrx=59/10*1/2#

#rarrx=59/20=2 19/20#