Chapter 6.3, Problem 4CYU

To determine

To solve the given system of equations using elimination method

Answer to Problem 4CYU

  $a=4$ and $b=-1$

Explanation of Solution

Given:

Equations:

  $6a-3b=27$

  $2a-3b=11$

Calculation:

Let,

  $\begin{array}{l}6a-3b=\mathrm{27.......}(i)\\ 2a-3b=\mathrm{11.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (2a-3b)-(6a-3b)=11-27\\ \Rightarrow 2a-3b-6a+3b=-16\\ \Rightarrow -4a=-16\\ \Rightarrow a=4\end{array}$

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

  $\begin{array}{l}\Rightarrow 6\times 4-3b=27\\ \Rightarrow 24-3b=27\\ \Rightarrow b=-1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $a=4$ and $b=-1$ .