Chapter 6.3, Problem 7PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 7PPS

  $v=-3$ and $w=4$

Explanation of Solution

Given:

Equations:

  $-v+w=7$

  $v+w=1$

Calculation:

Let,

  $\begin{array}{l}-v+w=\mathrm{7.......}(i)\\ v+w=\mathrm{1.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (-v+w)+(v+w)=7+1\\ \Rightarrow -v+w+v+w=8\\ \Rightarrow 2w=8\\ \Rightarrow w=4\end{array}$

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

  $\begin{array}{l}\Rightarrow -v+4=7\\ \Rightarrow v=-3\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $v=-3$ and $w=4.$