Chapter 6.3, Problem 41PFA

To determine

To find the solution to the given system of equations

Answer to Problem 41PFA

  $x=1.5$ and $y=7$

Explanation of Solution

Given:

Equations:

  $\begin{array}{l}-2x+y=4\\ 2x+y=10\end{array}$

Calculation:

Let,

  $\begin{array}{l}-2x+y=\mathrm{4.......}(i)\\ 2x+y=\mathrm{10.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (-2x+y)+(2x+y)=4+10\\ \Rightarrow -2x+y+2x+y=14\\ \Rightarrow 2y=14\\ \Rightarrow y=7\end{array}$

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

  $\begin{array}{l}\Rightarrow -2x+7=4\\ \Rightarrow -2x=4-7\\ \Rightarrow x=\frac{3}{2}=1.5\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=1.5$ and $y=7$ .