Question

How do you solve the system of equations: 3x+y=3 and x+2y=-4?

Answer 1

The solutions 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 the equations by elimination as `color(blue)(3x)` is common to both equations.

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

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

Finding `x` by substituting `y` in equation `2`
`x+2y=-4`
`x=-4-2y`
`x=-4-2*-3`
`x=-4+6`
`color(blue)(x=2`