Chapter 6.5, Problem 11PPS

To determine

To solve the given system of equations with the best method

Answer to Problem 11PPS

  $x=1$ and $y=3$

Explanation of Solution

Given:

Equations:

  $-5x+4y=7$

  $-5x-3y=-14$

From the above equations, it can be observed that the co-efficient of x 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,

  $\begin{array}{l}-5x+4y=\mathrm{7.......}(i)\\ -5x-3y=-\mathrm{14.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (-5x+4y)-(-5x-3y)=7-(-14)\\ \Rightarrow -5x+4y+5x+3y=21\\ \Rightarrow 7y=21\\ \Rightarrow y=3\end{array}$

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

  $\begin{array}{l}\Rightarrow -5x+4\times 3=7\\ \Rightarrow -5x=-5\\ \Rightarrow x=1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=1$ and $y=3$ .