How do solve the following linear system?: # -9x + 6y = -2 , x-3y=-2 #?

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Answer 1 · 2016-01-31T08:44:05

#(x,y)=(6/7,20/21)#

Solve by elimination:

#-9x+6y=-2#

#x-3y=-2#

We can eliminate #-9x# in the first equation by #x# in the second equation if we multiply it with #9# to get #9x#:

#rarr9(x-3y=-2)#

#rarr9x-27y=-18#

Now add both of the equations:

#rarr(-9x+6y=-2)+(9x-27y=-18)#

#rarr -21y=-20#

#rarry=(-20)/-21=20/21#

(Because,#(-n)/(-p)##=(+n)/(+p)#)

Substitute the value to the second equation:

#rarrx-3(20/21)=-2#

#rarrx-60/21=-2#

#rarrx-20/7=-2#

#rarrx=-2+20/7#

#rarrx=-14/7+20/7#

#rarrx=6/7#