Question

How do you solve using elimination of `3x+6y=12` and `2x-2.5y=13`?

Answer 1

The system has one dolution: `{(x=5 7/13),(y=-10/13):}`

Explanation:

The original system is:

`{(3x+6y=12),(2x-2.5y=13):}`

The elimination method means to change the system so that it is possible to eliminate one variable by adding (or substracting) both sides of the equations:

First we can divide both sides of the first equation by `3` to make all the coefficients smaller and multiply the second equation by `2` to make all the coefficients integer:

`{(x+2y=4),(4x-5y=26):}`

Now if we multiply the first equation by `(-4)` the coefficients of `x` will be opposite numbers (`4` and `-4`)

`{(-4x-8y=-16),(4x-5y=26):}`

Now if we add both sides of the equations the variable `x` will be eliminated:

`-13y=10`

`y=-10/13`

Now if we move `2y` to the right side of the first equation before the last multiplication we get:

`x=4-2y`

Now we only have to put calculated `y` in this equation and calculate `x`

`x=4-2*(-10/13)`

`x=4+20/13`

`y=(52+20)/13`

`y=72/13`

`y=5 7/13`