Question

How do you solve this system of equations: `4s - 3t = 8 and t = - 2s - 1`?

Answer 1

`(s,t)=(1/2,-2)`

Explanation:

Given
[1]`color(white)("XXX")4s-3t=8`
[2]`color(white)("XXX")t=-2s-1`

Based on [2] we can substitute `(-2s-1)` for `t` in [1]
[3]`color(white)("XXX")4s-3(-2s-1)=8`

Simplifying
[4]`color(white)("XXX")4s +6s+3=8`

[5]`color(white)("XXX")10s=5`

[6]`color(white)("XXX")s=1/2`

Substituting `1/2` for `s` in [2]
[7]`color(white)("XXX")t=-2 * (1/2) -1=-2`

Answer 2

`t=-2` and `s=-1/2`

Explanation:

the given two equations are
`4s-3t=8`
`t=-2s-1rArrt+2s=-1`
multiplying `2s+t=-1` by 3 we get
`3(2s+t=-1)rArr6s+3t=-3`
now on adding `(4s-3t=8)+(4s+3t=-3)`
we get `2s=1rArrs=1/2`
on substituting `s=1/2` in `4s-3t=8rArr4(1/2)-8=3trArr3t=-6rArrt=-2`
hence we get the answer `s=1/2 and t=-2`