Chapter 6.5, Problem 1CGP

To determine

To solve the given system of equations

Answer to Problem 1CGP

  $x=3$ and $y=-2$

Explanation of Solution

Given:

Equations:

  $5x-y=17$

  $3x+2y=5$

Calculation:

Let,

  $\begin{array}{l}5x-y=\mathrm{17.......}(i)\\ 3x+2y=\mathrm{5.......}(ii)\end{array}$

Now, add equation ( ii ) and $2\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 2\times (5x-y)+(3x+2y)=2\times (17)+(5)\\ \Rightarrow 10x-2y+3x+2y=39\\ \Rightarrow 13x=39\\ \Rightarrow x=3\end{array}$

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

  $\begin{array}{l}\Rightarrow 5\times (3)-y=17\\ \Rightarrow -y+15=17\\ \Rightarrow -y=2\\ \Rightarrow y=-2\end{array}$

Conclusion:

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