Chapter 6.3, Problem 18PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 18PPS

  $x=1$ and $y=2.5$

Explanation of Solution

Given:

Equations:

  $6x-2y=1$

  $10x-2y=5$

Calculation:

Let,

  $\begin{array}{l}6x-2y=\mathrm{1.......}(i)\\ 10x-2y=\mathrm{5.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (10x-2y)-(6x-2y)=5-1\\ \Rightarrow 10x-2y-6x+2y=4\\ \Rightarrow 4x=4\\ \Rightarrow x=1\end{array}$

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

  $\begin{array}{l}\Rightarrow 6\times 1-2y=1\\ \Rightarrow 6-2y=1\\ \Rightarrow y=2.5\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=1$ and $y=\mathrm{2.5.}$