Question

How do solve the following linear system?: `-6x-2y=-8 , 3x – 4y = 7`?

Answer 1

The solution for the system of equations is:
`color(blue)(x = 23/(15)`

`color(blue)(y = -3/5`

Explanation:

`color(green)(- 6x) - 2y = - 8` ......equation `(1)`

`3x - 4y = 7`, multiplying by `2`
`color(green)(6x) - 8y = 14`...............equation `(2)`

Solving by elimination:

Adding equations `1` and `2` eliminates `color(green)(6x.`

`cancelcolor(green)(- 6x) - 2y = - 8`
`cancelcolor(green)(6x) - 8y = 14`

`-10y = 6`

`y = - 6/10`

`color(blue)(y = -3/5`

Finding `x` from equation `2`:
`3x - 4y = 7`

`3x = 7 + 4y`

`3x = 7 + 4 * color(blue)((-3/5)`

`3x = 7 - 12/5`

`3x = 35/5 - 12/5`

`3x = 23/5`

`x = 23/(5 * 3)`

`color(blue)(x = 23/(15)`