Chapter 6.5, Problem 9PPS

To determine

To solve the given system of equations with the best method

Answer to Problem 9PPS

  $x=1$ and $y=-\frac{1}{2}$

Explanation of Solution

Given:

Equations:

  $5x+8y=1$

  $-2x+8y=-6$

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

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

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

Calculation:

Let,

  $\begin{array}{l}5x+8y=\mathrm{1.......}(i)\\ -2x+8y=-\mathrm{6.......}(ii)\end{array}$

Now, subtract equation ( ii ) from equation ( i ),

  $\begin{array}{l}\Rightarrow (5x+8y)-(-2x+8y)=1-(-6)\\ \Rightarrow 5x+8y+2x-8y=7\\ \Rightarrow 7x=7\\ \Rightarrow x=1\end{array}$

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

  $\begin{array}{l}\Rightarrow 5\times 1+8y=1\\ \Rightarrow 8y=-4\\ \Rightarrow y=-\frac{1}{2}\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=1$ and $y=-\frac{1}{2}$ .