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

##### 1 Answer
Aug 26, 2015

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
$\left(r , t\right) = \left(0.92 , 1.48\right)$

#### 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 $r$
$3 r - 2 t = - 0.2 \textcolor{w h i t e}{\text{XXXXXX")rarrcolor(white)("XX}} r = \frac{2 t - 0.2}{3}$
and
$r + s = 2.4 \textcolor{w h i t e}{\text{XXXXXXXXX")rarrcolor(white)("XX}} r = 2.4 - s$

So
$\textcolor{w h i t e}{\text{XX")(2t-0.2)/3 =2.4-scolor(white)("XX")rarrcolor(white)("XX}} 2 t - 7.2 s = 0.2$

If however the equations were meant to be (in only two variables):
[1]$\textcolor{w h i t e}{\text{XX}} 3 r - 2 t = - 0.2$
[2]$\textcolor{w h i t e}{\text{XX}} r + t = 2.4$

Multiplying [2] by 2:
[3]$\textcolor{w h i t e}{\text{XX}} 2 r + 2 t = 4.8$

Adding [1] and [3]
[4]$\textcolor{w h i t e}{\text{XX}} 5 r = 4.6$

Dividing by 5
[5]$\textcolor{w h i t e}{\text{XX}} r = 0.92$

Substituting $0.92$ for $r$ in [2]
[6]$\textcolor{w h i t e}{\text{XX}} 0.92 + t = 2.4$

Subtracting $0.92$ from both sides
[7]$\textcolor{w h i t e}{\text{XX}} t = 1.48$