Question

How do you solve the system using elimination `2x-y=9` and `x-2y=11`?

Answer 1

The solution for the system of equations is
`color(blue)( x =7/3 and y =-13/3`

Explanation:

`2x-y=9` , multiplying this equation by `2`
`4x color(blue)(-2y) =18`.......equation `(1)`
`xcolor(blue)(-2y)=11` ........equation `(2)`

Subtracting equation `(1)` from `(2)` to eliminate `color(blue)(2y`

`xcolor(blue)cancel(-2y)=11`
`-4x color(blue)cancel(+2y) =-18`

`-3x = -7`
`color(blue)(x = 7/3`

Substituting `x` in the first equation to find `y`

`y = 2x -9`

`y = 2.(7/3) - 9`

`y = 14/3 - 9`
`color(blue)( y = -13/3`