Chapter 6.5, Problem 1AGP

To determine

To solve the given system of equations

Answer to Problem 1AGP

$x=-1$ and $y=1$

Explanation of Solution

Given:

Equations:

$5x+7y=2$

$-2x+7y=9$

Calculation:

Let,

$\begin{array}{l}5x+7y=\mathrm{2.......}(i)\\ -2x+7y=\mathrm{9.......}(ii)\end{array}$

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

$\begin{array}{l}\Rightarrow (5x+7y)-(-2x+7y)=2-9\\ \Rightarrow 5x+7y+2x-7y=-7\\ \Rightarrow 7x=-7\\ \Rightarrow x=-1\end{array}$

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

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

Conclusion:

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