Chapter 6.4, Problem 16PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 16PPS

  $x=-6$ and $y=-8$

Explanation of Solution

Given:

Equations:

  $4x+7y=-80$

  $3x+5y=-58$

Calculation:

Let,

  $\begin{array}{l}8x+3y=\mathrm{4.......}(i)\\ -7x+5y=-\mathrm{34.......}(ii)\end{array}$

Now, subtract equation $7\times$ ( ii ) from $5\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 5\times (4x+7y)-7\times (3x+5y)=5\times (-80)-7\times (-58)\\ \Rightarrow 20x+35y-21x-35y=6\\ \Rightarrow -x=6\\ \Rightarrow x=-6\end{array}$

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

  $\begin{array}{l}\Rightarrow 4\times (-6)+7y=-80\\ \Rightarrow y=-8\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-6$ and $y=-8$ .