Question

How do you solve the following system?: `8x - 2y = - 4 , x + 2y = 6`

Answer 1

The solution is:
`x = 2/ 9`

`y = 26/ 9`

Explanation:

`8x color(blue)(- 2y) = -4`..........equation `(1)`

`x + color(blue)( 2y) =6`.................equation `(2)`

Solving by elimination:

Adding equations `(1)` and `(2)`

`8x color(blue)cancel(- 2y) = -4`

`x + cancelcolor(blue)( 2y) =6`

`9x = 2`

`x = 2/ 9`

Finding `y` by substituting the value `x` in equation `1`
`8x color(blue)(- 2y) = -4`

`8 * (2/9) color(blue)(- 2y) = -4`

`16/9 + 4 = 2y`

`16/9 + 36/9 = 2y`

`52/9 = 2y`

`52/(9 * 2 ) =y`

`y = cancel 52/( cancel18)`

`y = 26/9`