Chapter 6.5, Problem 1CYU

To determine

To solve the given system of equations with the best method

Answer to Problem 1CYU

  $x=2$and $y=-5$

Explanation of Solution

Given:

Equations:

  $2x+3y=-11$

  $-8x-5y=9$

From the above equations, it can be observed that the co-efficient of x in both the equation are four times in magnitude of each other with opposite sign.

Hence, it will be easy to eliminate them by just adding the equations after taking 4 times of first equation.

So, in this case elimination method will be more convenient and best.

Calculation:

Let,

  $\begin{array}{l}2x+3y=-\mathrm{11.......}(i)\\ -8x-5y=\mathrm{9.......}(ii)\end{array}$

Now, add equation (ii) and $4\times$ equation (i),

  $\begin{array}{l}\Rightarrow 4(2x+3y)+(-8x-5y)=4\times (-11)+9\\ \Rightarrow 8x+12y-8x-5y=-35\\ \Rightarrow 7y=-35\\ \Rightarrow y=-5\end{array}$

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

  $\begin{array}{l}\Rightarrow 2x+3\times (-5)=-11\\ \Rightarrow x=2\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=2$and $y=-5$.