How do solve the following linear system?: # 3x-2y=2 , -6x+5y=1 #?

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Answer 1 · 2016-02-01T10:10:55

Solve by substitution and elimination:

#3x-2y=2#

#-6x+5y=1#

We can eliminate #-6x# from the second equation by #3x# in the first equation if we multiply it with #2# to get #6x#.

#rarr2(3x-2y=2)#

#rarr=6x-4y=4#

Add both of the equations:

#rarr(-6x+5y=1)+(6x-4y=4)#

#rarr(5y=1)+(-4y=4)#

#rarry=5#

Substitute the value of #y# to the second equation:

#rarr-6x+5(5)=1#

#rarr-6x+25=1#

#rarr-6x=1-25#

#rarr-6x=-24#

#rarrx=(-24)/-6=24/6=4#

Because,#(-n)/-m=n/m#

So,#(x,y)=(4,5)#