Chapter 6.4, Problem 15PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 15PPS

  $x=1$ and $y=-5$

Explanation of Solution

Given:

Equations:

  $8x+3y=-7$

  $7x+2y=-3$

Calculation:

Let,

  $\begin{array}{l}8x+3y=-\mathrm{7.......}(i)\\ 7x+2y=-\mathrm{3.......}(ii)\end{array}$

Now, subtract equation $3\times$ (ii) from $2\times$ equation (i),

  $\begin{array}{l}\Rightarrow 2\times (8x+3y)-3\times (7x+2y)=2\times -7-3\times -3\\ \Rightarrow 16x+6y-21x-6y=-14+9\\ \Rightarrow -5x=-5\\ \Rightarrow x=1\end{array}$

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

  $\begin{array}{l}\Rightarrow 8\times 1+3y=-7\\ \Rightarrow y=-5\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=1$ and $y=-5$ .