Question

How do solve the following linear system?: `-x-7y=14 , x-2y=8`?

Answer 1

`(x,y)=(28/9,-22/9)`

Explanation:

Solve by elimination and substitution

`color(blue)(-x-7y=14`

`color(blue)(x-2y=8`

We can eliminate `x` in the first equation by `-x` in the second equation

Add both the equations

`rarr(-x-7y=14)+(x-2y=8)`

`rarr-9y=22`

`color(green)(rArry=-22/9`

Substitute the value of `y` to the second equation

`rarrx-2(-22/9)=8`

`rarrx+44/9=8`

`color(green)(rArrx=8-44/9=28/9`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Check (`-x-7y=14`)

`rarr-28/9-7(-22/9)=14`

`rarr-28/9+154/9=14`

`rarr(-28+154)/9=14`

`rarr126/9=14`

`color(orange)(rArr14=14`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Check (`x-2y=8`)

`rarr28/9-2(-22/9)=8`

`rarr28/9+44/9=8`

`rarr(28+44)/9=8`

`rarr72/9=8`

`color(violet)(rArr8=8`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

`:. color(blue)( ul bar |(x,y)=28/9,-22/9|`