How do you solve the following linear system x+y= -3, 3x+y=3 x+y=−3,3x+y=3?

1 Answer
Shwetank Mauria
Sep 4, 2016

x=3x=3 and y=-6y=−6

Explanation:

There are many methods for solving pair of linear equations in two variables. Prominent among them is substitution method.

First equation x+y=-3x+y=−3 gives us x=-y-3x=−y−3. Putting this in second equation we get

3×(-y-3)+y=33×(−y−3)+y=3 or

-3y-9+y=3−3y−9+y=3 or

-2y=3+9=12−2y=3+9=12 i.e. y=-6y=−6 and x=-(-6)-3=6-3=3x=−(−6)−3=6−3=3

Another method could be multiplying first equation by 33 which gives us 3x+3y=-93x+3y=−9. Now subtracting second equation 3x+y=33x+y=3 from this, we get 2y=-122y=−12 or y=-6y=−6. Putting this in first we get x-6=-3x−6=−3 i.e. x=3x=3.

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