Chapter 6.4, Problem 22PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 22PPS

  $x=4.5$and $y=-1.5$

Explanation of Solution

Given:

Equations:

  $-0.4x+0.25y=-2.175$

  $2x+y=7.5$

Calculation:

Let,

  $\begin{array}{l}-0.4x+0.25y=-\mathrm{2.175.......}(i)\\ 2x+y=\mathrm{7.5.......}(ii)\end{array}$

Now, subtract equation $0.25\times$ ( ii ) from equation ( i ),

  $\begin{array}{l}\Rightarrow (-0.4x+0.25y)-0.25\times (2x+y)=-2.175-0.25\times 7.5\\ \Rightarrow -0.4x+0.25y-0.5x-0.25y=-4.05\\ \Rightarrow -0.9x=-4.05\\ \Rightarrow x=4.5\end{array}$

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

  $\begin{array}{l}\Rightarrow -0.4\times (4.5)+0.25y=-2.175\\ \Rightarrow y=-1.5\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=4.5$and $y=-1.5$ .