Chapter 4.5, Problem 42PPS

To determine

To find: The solution of equations using Cramer’s rule.

Answer to Problem 42PPS

The solution of the system is (5,-1).

Explanation of Solution

Given,

The set of equation is given as,

  $\begin{array}{l}-6f-8g=-22\\ -11f+5g=-60\end{array}$

Calculation:

Calculate the value of x using Cramer’s rule.

  $\begin{array}{c}x=\frac{\left|\begin{array}{cc}-22& -8\\ -60& 5\end{array}\right|}{\left|\begin{array}{cc}-6& -8\\ -11& 5\end{array}\right|}\\ =\frac{-22\left(5\right)-\left(-60\right)\left(-8\right)}{-6\left(5\right)-\left(-11\right)\left(-8\right)}\\ =\frac{-590}{-118}\\ =5\end{array}$

Calculate the value of yusing Cramer’s rule.

  $\begin{array}{c}y=\frac{\left|\begin{array}{cc}-6& -22\\ -11& -60\end{array}\right|}{\left|\begin{array}{cc}-6& -8\\ -11& 5\end{array}\right|}\\ =\frac{-6\left(-60\right)-\left(-11\right)\left(-22\right)}{-6\left(5\right)-\left(-11\right)\left(-8\right)}\\ =\frac{118}{-118}\\ =-1\end{array}$

Thus, the solution of the system is (5,-1).