Question

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

Answer 1

`x=3` and `y=-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=-3` gives us `x=-y-3`. Putting this in second equation we get

`3×(-y-3)+y=3` or

`-3y-9+y=3` or

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

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