How do you solve the following linear system: # -x+2y=-6 , 6x-y=-35 #?

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Answer 1 · 2017-09-02T15:23:30

#(-76/11 , -71/11)#

#-x+2y=-6#
#6x-y=-35#

Let's use linear combination to solve this system.

We will begin by multiplying the second system by #2#.

#12x-2y=-70#

Then, we will add the two equations together. This works because we add #-70# to one side and add #(12x-2y)#, an equivalent value, to the other side.

#11x=-76#
#x=-76/11#

Then we'll find, in either equation, the output #y# value for this value of #x#.

#-(color(red)(-76/11))+2y=-6#
#color(red)(76/11)+2y=-6#
#2y=color(red)(-142/11)#
#y=-71/11#

These systems intersect at the point #(-76/11 , -71/11)#

This solution is pretty ugly, so let's check to make sure it's correct.
We'll use #6x-y=-35#, and substitute #-71/11# for #y#

#6x-(color(red)(-71/11))=-35#
#6xcolor(red)(+71/11)=-35#
#6x=color(red)(-456/11)#
#x=-76/11#

So our solution is #(-76/11 , -71/11)#.