91Ó°ÊÓ

Multiply the equation $-r-3s+2t=-2$by 2 and add the new resultant equation to $2r+s+t=14$.

$\begin{array}{l}\underset{¯}{\begin{array}{l}−\text{ }r−3s+2t=−\text{ â¶Ä„}2\\ \text{ }2r+\text{ â¶Ä„}s\text{ }+\text{ â¶Ä„ }t=\text{ â¶Ä„  }14\end{array}}\text{ â¶Ä„ â¶Ä„}\begin{array}{c}\text{multiplyby2}→\\ \end{array}\text{ â¶Ä„}\underset{¯}{\begin{array}{l}−2r−6s+4t=−4\\ \text{ â¶Ä„}2r+\text{ â¶Ä„}s\text{ }+\text{ â¶Ä„}t=14\end{array}}\\ \text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„}0−5s+5t=10\end{array}$

Simplify $-5s+5t=10$:

$\begin{array}{c}−5s+5t=10\\ −s+t=2\text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„dividebothsidesby5}\end{array}$

So, the resultant equation is $-s+t=2$.

Next, multiply the equation $-r-3s+2t=-2$by 4and add the new resultant equation to $4r-6s+3t=-5$.

$\begin{array}{l}\underset{¯}{\begin{array}{l}−\text{ }r−3s+2t=−2\\ \text{ }4r−6s\text{ }+3t=−5\end{array}}\text{ â¶Ä„ â¶Ä„}\begin{array}{c}\text{multiplyby4}→\\ \end{array}\text{ â¶Ä„}\underset{¯}{\begin{array}{l}−4r−12s+8t=−8\\ \text{ â¶Ä„}4r−\text{ â¶Ä„}6s+3t=−5\end{array}}\\ \text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„}0−18s+11t=−13\end{array}$

So, the resultant equation is $-18s+11t=-13$.

Multiply $-s+t=2$by 18 and subtract the new resultant equation from $-18s+11t=-13$.

$\begin{array}{l}\underset{¯}{\begin{array}{l}−\text{ â¶Ä„  â¶Ä„}s+\text{ â¶Ä„ }t=\text{ â¶Ä„ â¶Ä„}2\\ −18s+11t=−13\end{array}}\text{ â¶Ä„ â¶Ä„}\begin{array}{c}\text{multiplyby18}\\ \end{array}\text{ â¶Ä„}\underset{¯}{\begin{array}{l}\text{ â¶Ä„ â¶Ä„}−18s+18t=\text{ â¶Ä„ }36\\ \left(−\right)−18s+11t=−13\end{array}}\\ \text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ }0+\text{ â¶Ä„}7t=\text{ â¶Ä„ }49\end{array}$

Solve $7t=49$for $t$:

$\begin{array}{c}7t=49\\ \frac{7t}{7}=\frac{49}{7}\text{ â¶Ä„ â¶Ä„ â¶Ä„Dividebothsidesby7}\\ t=7\end{array}$

Substitute $t=7$in $-s+t=2$and find the value of $s$.

$\begin{array}{c}−s+t=2\\ −s+7=2\text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ Substitute7for}t\\ −s=−5\text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ Subtract7frombothsides}\\ s=5\text{ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ â¶Ä„ Dividebothsidesby-1}\end{array}$

Substitute $s=5,t=7$in $-r-3s+2t=-2$and find the value of r.

Hence, the solution of the given system of equations is $\left(r,s,t\right)=\left(1,5,7\right)$.