Question

How do solve the following linear system?: `3x-y=7 , 11x + 3y + 7 = 0`?

Answer 1

The solution for the system of equations is:
`color(green)(x = 7 / 10`

`color(green)(y = (- 49) / 10`

Explanation:

`3x - y = 7` , multiplying by `3`
`9x - color(blue)(3y )= 21`.....................equation `(1)`

`11x + color(blue)( 3y) = - 7`................equation `(2)`

Solving by elimination.

Adding equations `1` and `2` eliminates `color(blue)(3y`

`9x - cancelcolor(blue)(3y )= 21`

`11x + cancelcolor(blue)( 3y) = - 7`

`20x = 14`

`x = 14 / 20`

`color(green)(x = 7 / 10`

Finding `y` from equation `1`

`3x - y = 7`

`3x - 7 = y`

`3 * color(green)(7/10) - 7 = y`

`21/10 - 7 = y`

`(21 - 70) / 10 = y`

`(- 49) / 10 = y`

`color(green)(y = (- 49) / 10`