Chapter 6.4, Problem 1CYU

To determine

To solve the given system of equations using elimination method

Answer to Problem 1CYU

  $x=3$ and $y=2$

Explanation of Solution

Given:

Equations:

  $2x-y=4$

  $7x+3y=27$

Calculation:

Let,

  $\begin{array}{l}2x-y=\mathrm{4.......}(i)\\ 7x+3y=\mathrm{27.......}(ii)\end{array}$

Now, add equation $3\times$ ( i ) and equation ( ii ),

  $\begin{array}{l}\Rightarrow 3(2x-y)+(7x+3y)=4\times 3+27\\ \Rightarrow 6x-3y+7x+3y=39\\ \Rightarrow 13x=39\\ \Rightarrow x=3\end{array}$

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

  $\begin{array}{l}\Rightarrow 2\times 3-y=4\\ \Rightarrow 6-y=4\\ \Rightarrow y=2\end{array}$

Conclusion:

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