Chapter 6.4, Problem 21PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 21PPS

  $x=2.5$ and $y=3.25$

Explanation of Solution

Given:

Equations:

  $2.2x+3y=15.25$

  $4.6x+2.1y=18.325$

Calculation:

Let,

  $\begin{array}{l}2.2x+3y=\mathrm{15.25.......}(i)\\ 4.6x+2.1y=\mathrm{18.325.......}(ii)\end{array}$

Now, subtract equation ( ii ) from $0.7\times$ equation ( i ),

  $\begin{array}{l}\Rightarrow 0.7\times (2.2x+3y)-(4.6x+2.1y)=0.7\times 15.25-18.325\\ \Rightarrow 1.54x+2.1y-4.6x-2.1y=10.675-18.325\\ \Rightarrow -3.06x=-7.65\\ \Rightarrow x=2.5\end{array}$

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

  $\begin{array}{l}\Rightarrow 2.2\times (2.5)+3y=15.25\\ \Rightarrow y=3.25\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=2.5$ and $y=3.25$ .