Question

How do you solve the following linear system `2x-y=4, x+3y=1?`?

Answer 1

Solve for one term with respect to another, then solve for the second term, then back-solve for the first. You will find that `x=13/7` and `y=-2/7`

Explanation:

First, we'll want to solve for either `x` in terms of `y` or vice versa. For the sake of argument, we'll sove for `x` in terms of `y` using the second expression:

`x+3y=1`

`rArrcolor(blue)(x=1-3y)`

Now, we take that solution for `x` and substitute it in, in expression 1:

`2color(blue)(x)-y=4`

`2color(blue)((1-3y))-y=4`

`2-6y-y=4`

`2-7y=4`

`-7y=2`

`color(green)(y=-2/7)`

We now have a solution for `y`. We can then plug it into either expression to solve for `x`:

`x+3color(green)(y)=1`

`x+3color(green)((-2/7))=1`

`x-6/7=1`

`x=1+6/7`

`color(green)(x=13/7)`

And now we have our solution:

`x=13/7`, `y=-2/7`