Chapter 6.4, Problem 8PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 8PPS

$x=-2$ and $y=6$

Explanation of Solution

Given:

Equations:

$x-y=-8$

$7x+5y=16$

Calculation:

Let,

$\begin{array}{l}x-y=-\mathrm{8.......}(i)\\ 7x+5y=\mathrm{16.......}(ii)\end{array}$

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

$\begin{array}{l}\Rightarrow (7x+5y)+5\times (x-y)=16+5\times (-8)\\ \Rightarrow 7x+5y+5x-5y=-24\\ \Rightarrow 12x=-24\\ \Rightarrow x=-2\end{array}$

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

$\begin{array}{l}\Rightarrow -2-y=-8\\ \Rightarrow y=6\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-2$ and $y=6$ .