Chapter 6.4, Problem 11PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 11PPS

  $x=-2$ and $y=3$

Explanation of Solution

Given:

Equations:

  $2x+5y=11$

  $4x+3y=1$

Calculation:

Let,

  $\begin{array}{l}2x+5y=\mathrm{11.......}(i)\\ 4x+3y=\mathrm{1.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow 2\times (2x+5y)-(4x+3y)=2\times 11-1\\ \Rightarrow 4x+10y-4x-3y=21\\ \Rightarrow 7y=21\\ \Rightarrow y=3\end{array}$

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

  $\begin{array}{l}\Rightarrow 2x+5\times 3=11\\ \Rightarrow x=-2\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-2$ and $y=3$ .