Chapter 6.5, Problem 3CYU

To determine

To solve the given system of equations with the best method

Answer to Problem 3CYU

  $x=-\frac{1}{3}$ and $y=1$

Explanation of Solution

Given:

Equations:

  $3x-4y=-5$

  $-3x+2y=3$

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

Hence, it will be easy to eliminate them by just adding both the equations.

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

Calculation:

Let,

  $\begin{array}{l}3x-4y=-\mathrm{5.......}(i)\\ -3x+2y=\mathrm{3.......}(ii)\end{array}$

Now, add equation ( i ) and equation ( ii ),

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

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

  $\begin{array}{l}\Rightarrow 3x-4\times 1=-5\\ \Rightarrow 3x=-1\\ \Rightarrow 3x=-1\\ \Rightarrow x=\frac{-1}{3}\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-\frac{1}{3}$ and $y=1$ .