Question

Solve each system of equations.

6.

$\begin{array}{l}r-3s+t=4\\ 3r-6s+9t=5\\ 4r-9s+10t=9\end{array}$

Short answer

The solution has infinitely many solutions.

Step-by-step solution

Step-1 –Using elimination to obtain two equations in two variables

Given system of equations are

$\begin{array}{l}r-3s+t=4\\ 3r-6s+9t=5\\ 4r-9s+10t=9\end{array}$

Multiplying first equation by $3$and subtracting with the second equation, we get

$\begin{array}{l}-12s+9s+4t-10t=16-9\\ -3s-6t=7\end{array}$

Step-2 –Solving the system of two equations in two variables

System of equations with two variables are

$\begin{array}{l}-3s-6t=7\\ -3s-6t=7\end{array}$

Therefore, the equation $-3s-6t=7$has infinitely many solutions.

Step-3 –Evaluating the value of r

Since, $s$and $t$has infinitely many values and so $r$has many values.