How do solve the following linear system?: # x - 3y = -6 , 10x - 7y = -18 #?

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Answer 1 · 2016-01-27T14:13:19

#{x,y}={-12/23,42/23}#

Solve by elimination

#x-3y=-6#
#10x-7y=-18#

We can eliminate #10x# from the second equation by #x# in the first equation if we multiply #x# by #-10# to get #-10x#

#rarr-10(x-3y=-6)#

#rarr-10x+30y=60#

Now add both of the equations

#rarr(-10x+30y=60)+(10x-7y=-18)#

#rarr23y=42#

#y=42/23#

Now substitute the value of y to the first equation

#x-3(42/23)=-6#

#x-126/23=-6#

#x=-6+126/23=(-138+126)/23=-12/23#

So,#{x,y}={-12/23,42/23}#