Chapter 6.4, Problem 7PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 7PPS

  $x=-1$ and $y=3$

Explanation of Solution

Given:

Equations:

  $x+y=2$

  $-3x+4y=15$

Calculation:

Let,

  $\begin{array}{l}x+y=\mathrm{2.......}(i)\\ -3x+4y=\mathrm{15.......}(ii)\end{array}$

Now, add equation $3\times$ ( i ) and equation ( ii ),

  $\begin{array}{l}\Rightarrow 3\times (x+y)+(-3x+4y)=3\times 2+15\\ \Rightarrow 3x+3y-3x+4y=6+15\\ \Rightarrow 7y=21\\ \Rightarrow y=3\end{array}$

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

  $\begin{array}{l}\Rightarrow x+3=2\\ \Rightarrow x=-1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=-1$ and

  $y=3$