Chapter 6.3, Problem 17PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 17PPS

  $x=4$ and $y=1.5$

Explanation of Solution

Given:

Equations:

  $-3x-8y=-24$

  $3x-5y=4.5$

Calculation:

Let,

  $\begin{array}{l}-3x-8y=-\mathrm{24.......}(i)\\ 3x-5y=\mathrm{4.5.......}(ii)\end{array}$

Now, add equation ( i ) and equation ( ii ),

  $\begin{array}{l}\Rightarrow (-3x-8y)+(3x-5y)=-24+4.5\\ \Rightarrow -3x-8y+3x-5y=-19.5\\ \Rightarrow -13y=-19.5\\ \Rightarrow y=1.5\end{array}$

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

  $\begin{array}{l}\Rightarrow -3x-8\times 1.5=-24\\ \Rightarrow -3x-12=-24\\ \Rightarrow x=4\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=4$ and $y=\mathrm{1.5.}$