Chapter 6.4, Problem 2CYU

To determine

To solve the given system of equations using elimination method

Answer to Problem 2CYU

  $x=-3$ and $y=1$

Explanation of Solution

Given:

Equations:

  $2x+7y=1$

  $x+5y=2$

Calculation:

Let,

  $\begin{array}{l}2x+7y=\mathrm{1.......}(i)\\ x+5y=\mathrm{2.......}(ii)\end{array}$

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

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

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

  $\begin{array}{l}\Rightarrow 2x+7\times 1=1\\ \Rightarrow 2x+7=1\\ \Rightarrow x=-3\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-3$ and $y=1$ .