Question

How do you solve the simultaneous equations `3r - 2t = -0.2` and `r + s = 2.4`?

Answer 1

You can not solve for the values of 3 variables with only 2 equations;
however, if the second equation was meant to be `r+t=2.4` then
`(r,t)=(0.92,1.48)`

Explanation:

The best we could do with 2 equations with 3 unknowns is generate a linear relationship between two of the variables:
For example, by solving for `r`
`3r-2t = -0.2color(white)("XXXXXX")rarrcolor(white)("XX")r=(2t-0.2)/3`
and
`r+s= 2.4color(white)("XXXXXXXXX")rarrcolor(white)("XX")r= 2.4-s`

So
`color(white)("XX")(2t-0.2)/3 =2.4-scolor(white)("XX")rarrcolor(white)("XX")2t-7.2s = 0.2`

If however the equations were meant to be (in only two variables):
[1]`color(white)("XX")3r-2t= -0.2`
[2]`color(white)("XX")r+t= 2.4`

Multiplying [2] by 2:
[3]`color(white)("XX")2r+2t=4.8`

Adding [1] and [3]
[4]`color(white)("XX")5r= 4.6`

Dividing by 5
[5]`color(white)("XX")r=0.92`

Substituting `0.92` for `r` in [2]
[6]`color(white)("XX")0.92+t=2.4`

Subtracting `0.92` from both sides
[7]`color(white)("XX")t = 1.48`