Chapter 6.5, Problem 6PPS

To determine

To solve the given system of equations with the best method

Answer to Problem 6PPS

  $x=2$and $y=3$

Explanation of Solution

Given:

Equations:

  $-3x+y=-3$

  $4x+2y=14$

From the above equations, it can be observed that the co-efficient of y in both the equation are of 2 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 twice of the first equation.

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

Calculation:

Let,

  $\begin{array}{l}-3x+y=-\mathrm{3.......}(i)\\ 4x+2y=\mathrm{14.......}(ii)\end{array}$

Now, subtract equation ( ii ) from $2\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 2\times (-3x+y)-(4x+2y)=2\times (-3)-14\\ \Rightarrow -6x+2y-4x-2y=-20\\ \Rightarrow -10x=-20\\ \Rightarrow x=2\end{array}$

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

  $\begin{array}{l}\Rightarrow -3\times 2+y=-3\\ \Rightarrow y=3\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=2$and $y=3$ .