Question

How do you solve `3x+y=3` and `x+2y=-4`?

Answer 1

The solutions for the equation are
`color(blue)(x=2,y=-3`

Explanation:

`color(blue)(3x)+y=3`.................. equation `(1)`

`x+2y=−4`, multiplying this equation by `3`
`color(blue)(3x)+6y=−12`....... equation `(2)`

Now we can solve through elimination as term `color(blue)(3x)` is common to both equations.

Subtracting equation `(2)` from `(1)`
`cancel(color(blue)(3x))+y=3`
`-cancel(color(blue)(3x))-6y=+12`

`-5y=15`
`color(blue)(y=-3`

Substituting the value of `y` in equation `1`
`x+2y=−4`
`x+2 * (-3)=−4`
`x-6=−4`
`color(blue)(x=2`