Question

How do solve the following linear system?: `x+2y=1 , -2x -8y = 4`?

Answer 1

`x=4` and `y=-3/2` or `-1 1/2`

Explanation:

`x+2y=1`
`-2x-8y=4`

Reduce the second equation by dividing all terms by `2`.

`-2x-8y=4`

`-x-4y=2`

Multiply all terms by `-1`.

`x+4y=-2`

Separate `4y` into two.

`x+2y+2y=-2`

In this equation, substitute `(x+2y)` with `color(red)(1)`, the value from the first equation.

`x+2y+2y=-2`

`color(red)(1)+2y=-2`

Subtract `1` from both sides.

`2y=-3`

Divide both sides by `2`.

`y=-3/2=-1 1/2`

In the first equation, substitute `y` with `color(blue)(-3/2)`.

`x+2y=1`

`x+2color(blue)((-3/2))=1`

Open the brackets and simplify.

`x-3=1`

Add `3` to both sides.

`x=4`

Answer 2

`y=-1 1/2, x=4`

Explanation:

`x+2y=1`-----------(1)

`-2x-8y=4`---------(2)

`2x+4y=2` `(1) xx 2` ---------(3)

`-4y=6`--------(2)+(3)

`4y=-6`

`y=-6/4`

`y=-1 1/2`

Substitute `y=-6/4` in ----------1

`x+2(-6/4)=1`

`x-12/4=1`

`x-3=1`

`x=1+3`

`x=4`
Substitute #y= -6/4,x=4 in------1

`4+2(-6/4)=1`

`4-12/4=1`

multiply both sides by 4
`16-12=4`

`4=4`