Chapter 6.5, Problem 2CYU

To determine

To solve the given system of equations with the best method

Answer to Problem 2CYU

  $x=-3$and $y=5$

Explanation of Solution

Given:

Equations:

  $3x+4y=11$

  $2x+y=-1$

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

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

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

Calculation:

Let,

  $\begin{array}{l}3x+4y=\mathrm{11.......}(i)\\ 2x+y=-\mathrm{1.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow 4(2x+y)-(3x+4y)=-1\times 4-11\\ \Rightarrow 8x+4y-3x-4y=-15\\ \Rightarrow 5x=-15\\ \Rightarrow x=-3\end{array}$

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

  $\begin{array}{l}\Rightarrow 3\times -3+4y=11\\ \Rightarrow y=5\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-3$and $y=5$ .