Chapter 6.4, Problem 13PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 13PPS

  $x=3$ and $y=5$

Explanation of Solution

Given:

Equations:

  $3x+4y=29$

  $6x+5y=43$

Calculation:

Let,

  $\begin{array}{l}3x+4y=\mathrm{29.......}(i)\\ 6x+5y=\mathrm{43.......}(ii)\end{array}$

Now, subtract equation ( ii ) from $2\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 2\times (3x+4y)-(6x+5y)=2\times 29-43\\ \Rightarrow 6x+8y-6x-5y=15\\ \Rightarrow 3y=15\\ \Rightarrow y=5\end{array}$

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

  $\begin{array}{l}\Rightarrow 3x+5\times 4=29\\ \Rightarrow x=3\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=3$ and $y=5$ .