Question

How do solve the following linear system?: `-4x + 4 = -y, 3x + 6y + 13 = 0`?

Answer 1

`x = 11/27 and y = -2 17/27`

Explanation:

It might be better to work on the first equation a little and multiply by `-1` so the `y` term is positive. Then we have an equation which is suitable for the substitution method:

`-4x +4 = -y" "rarr (xx-1)" "rarrcolor(blue)(4x-4 = y)`

Substitute `color(blue)((4x-4))` for `y` in the other equation:

`3x+6color(blue)( y) +13=0`

`3x+6color(blue)((4x-4)) +13=0" "larr` only `x` terms

`3x+24x = -13+24`

`27x = 11`

`x = 11/27`

Now use `x=11/27` to find a value for `y`

`y =4x-4 = 4(11/27)-4`

`y= -2 10/27`

Checking into the second equation confirms these results:
`0=0`