Question

How do you solve the system of equations `r+ 4s = - 4` and `- 3r + 5s = 12`?

Answer 1

`r = -4 and s =0`

Explanation:

You have a choice of methods.. elimination or substitution

Substitution is a good option - there is a single `r` term

`" "-3color(red)(r) +5s =12" and "color(red)(r =-4s-4)`
`color(white)(xxx.x)darr`
`-3color(red)((-4s-4)) +5s =12`

`" "12s+12 +5s=12`

`17s = 12-12`

`17s = 0`

`s = 0 color(white)(.......................................)rarr r = -4s-4`

`color(white)(......................................................) r = 0-4`

`color(white)(......................................................) r =-4`