Chapter 6.3, Problem 11PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 11PPS

  $a=4$ and $b=-2$

Explanation of Solution

Given:

Equations:

  $a+4b=-4$

  $a+10b=-16$

Calculation:

Let,

  $\begin{array}{l}a+4b=-\mathrm{4.......}(i)\\ a+10b=-\mathrm{16.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (a+10b)-(a+4b)=-16-(-4)\\ \Rightarrow a+10b-a-4b=-12\\ \Rightarrow 6b=-12\\ \Rightarrow b=-2\end{array}$

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

  $\begin{array}{l}\Rightarrow a+4\times (-2)=-4\\ \Rightarrow a=4\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $a=4$ and $b=-2.$