Chapter 4.5, Problem 16CYU

To determine

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

Answer to Problem 16CYU

The solution of the system is (8, -3).

Explanation of Solution

Given,

The set of equation is given as,

  $\begin{array}{l}10c-7d=-59\\ 6c+5d=-63\end{array}$

Calculation:

Calculate the value of c using Cramer’s rule.

  $\begin{array}{c}c=\frac{\left|\begin{array}{cc}-59& -7\\ -63& 5\end{array}\right|}{\left|\begin{array}{cc}10& -7\\ 6& 5\end{array}\right|}\\ =\frac{-59\left(5\right)-\left(-63\right)\left(-7\right)}{10\left(5\right)-\left(6\right)\left(-7\right)}\\ =\frac{-736}{92}\\ =8\end{array}$

Calculate the value of d using Cramer’s rule.

  $\begin{array}{c}d=\frac{\left|\begin{array}{cc}10& -59\\ 6& -63\end{array}\right|}{\left|\begin{array}{cc}10& -7\\ 6& 5\end{array}\right|}\\ =\frac{10\left(-63\right)-\left(6\right)\left(-59\right)}{10\left(5\right)-\left(6\right)\left(-7\right)}\\ =\frac{-276}{92}\\ =-3\end{array}$

Thus, the solution of the system is (8, -3).