Chapter 6.3, Problem 13PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 13PPS

  $c=8$ and $d=-7$

Explanation of Solution

Given:

Equations:

  $6c-9d=111$

  $5c-9d=103$

Calculation:

Let,

  $\begin{array}{l}6c-9d=\mathrm{111.......}(i)\\ 5c-9d=\mathrm{103.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (6c-9d)-(5c-9d)=111-103\\ \Rightarrow 6c-9d-5c+9d=8\\ \Rightarrow c=8\end{array}$

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

  $\begin{array}{l}\Rightarrow 6\times (8)-9d=111\\ \Rightarrow 48-9d=111\\ \Rightarrow d=-7\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $c=8$ and $d=-7.$