Chapter 6.4, Problem 2AGP

To determine

To solve the given system of equations

Answer to Problem 2AGP

  $x=0$ and $y=-2$

Explanation of Solution

Given:

Equations:

  $5x-3y=6$

  $2x+5y=-10$

Calculation:

Let,

  $\begin{array}{l}5x-3y=\mathrm{6.......}(i)\\ 2x+5y=-\mathrm{10.......}(ii)\end{array}$

Now, add $5\times$ equation ( i ) and $3\times$ equation ( ii ),

  $\begin{array}{l}\Rightarrow 5(5x-3y)+3(2x+5y)=5\times (6)+3\times (-10)\\ \Rightarrow 25x-15y+6x+15y=30-30\\ \Rightarrow 31x=0\\ \Rightarrow x=0\end{array}$

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

  $\begin{array}{l}\Rightarrow 5\times 0-3y=6\\ \Rightarrow -3y=6\\ \Rightarrow y=-2\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=0$ and $y=-2$ .