Chapter 6.3, Problem 1ACYP

To determine

To solve the given system of equations

Answer to Problem 1ACYP

  $x=0$ and $y=-1$

Explanation of Solution

Given:

Equations:

  $-4x+3y=-3$

  $4x-5y=5$

Calculation:

Let,

  $\begin{array}{l}-4x+3y=-\mathrm{3.......}(i)\\ 4x-5y=\mathrm{5.......}(ii)\end{array}$

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

  $\begin{array}{l}\Rightarrow (-4x+3y)+(4x-5y)=-3+5\\ \Rightarrow -4x+3y+4x-5y=2\\ \Rightarrow -2y=2\\ \Rightarrow y=-1\end{array}$

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

  $\begin{array}{l}\Rightarrow -4x+3\times (-1)=-3\\ \Rightarrow -4x-3=-3\\ \Rightarrow x=0\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=0$ and $y=-1$ .