Chapter 6.3, Problem 12PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 12PPS

  $r=-3$ and $t=-4$

Explanation of Solution

Given:

Equations:

  $6r-6t=6$

  $3r-6t=15$

Calculation:

Let,

  $\begin{array}{l}6r-6t=\mathrm{6.......}(i)\\ 3r-6t=\mathrm{15.......}(ii)\end{array}$

Now, subtract equation ( i ) from equation ( ii ),

  $\begin{array}{l}\Rightarrow (3r-6t)-(6r-6t)=15-6\\ \Rightarrow 3r-6t-6r+6t=9\\ \Rightarrow -3r=9\\ \Rightarrow r=-3\end{array}$

Now, substitute the value of r in equation ( i ),

  $\begin{array}{l}\Rightarrow 6\times (-3)-6t=6\\ \Rightarrow -18-6t=6\\ \Rightarrow t=-4\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is

  $r=-3$ and $t=-4.$