Question

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

Answer 1

`x=-12 and y=8`

Explanation:

Here ,

`x+y=-4`

`:.y=-x-4.....to(1)`

`2x+4y=8...........to(2)`

Subst. `y=-x-4` into `(2)`, we get

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

`:.2x-4x-16=8`

`:.-2x=16+8`

`:.-2x=24`

`:.color(blue)(x=-12`

Subst.`x=-12` into `(1)`

`y=-(-12)-4=12-4`

`:.color(blue)(y=8`

Hence , `x=-12 and y=8`

Answer 2

`x=-12`
`y=8`

Explanation:

`x+y=-4` so `x=-4-y`

Substitute this into the second equation

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

Multiply out the bracket

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

Add 8 to both sides

`2y=16`

Divide by 2

`y=8`

Now put `y=8` into `x+y=-4`

`x+8=-4`

Subtract 8 from both sides

`x=-12`