Chapter 6.3, Problem 1BGP

To determine

To solve the given system of equations

Answer to Problem 1BGP

  $x=6$ and $y=1$

Explanation of Solution

Given:

Equations:

  $4y+3x=22$

  $3x-4y=14$

Calculation:

Let,

  $\begin{array}{l}4y+3x=\mathrm{22.......}(i)\\ 3x-4y=\mathrm{14.......}(ii)\end{array}$

Now, subtract equation ( i ) from equation ( ii ),

  $\begin{array}{l}\Rightarrow (4y+3x)+(3x-4y)=22+14\\ \Rightarrow 4y+3x+3x-4y=36\\ \Rightarrow 6x=36\\ \Rightarrow x=6\end{array}$

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

  $\begin{array}{l}\Rightarrow 4y+3\times 6=22\\ \Rightarrow 4y+18=22\\ \Rightarrow 4y=4\\ \Rightarrow y=1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=6$ and $y=1$ .