How do solve the following linear system?: -4x-15y=-1 , -3x+7y=-1 −4x−15y=−1,−3x+7y=−1?

1 Answer
georgef
Jul 31, 2016

The same values of xx and yy must satisfy both equations

Explanation:

Probably the easiest way to solve this is to manipulate the equations to bring them to a more convenient form in which both have the same coefficient for xx. Multiply the fist one by 33 and the second one by 44:

-12x-45y=-3−12x−45y=−3
-12x+28y=-4−12x+28y=−4

This system is equivalent to the given one. Now we subtract the second form the first, and we get:
-73y=1−73y=1, and then y=-1/73y=−173. Now replacing the yy value in either equation, say the first one, we have:

-12x-45*1/73=-3−12x−45⋅173=−3, so

-12x=-3+45/73−12x=−3+4573 so

-12x=(-219+45)/73−12x=−219+4573, and then

-12x=-174/73−12x=−17473, and this results in

x=(-1/12) * (-174/73)x=(−112)⋅(−17473), and simplifying

x=29/146x=29146

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