Chapter EP, Problem 4.5.11EP

To determine

The solution of the system of equations by using the Cramer’s rule.

Answer to Problem 4.5.11EP

  $(0.67,0.6)$ .

Explanation of Solution

Given information:

The system of equations:

  $\begin{array}{l}6c+5d=7\\ 3c-10d=-4\end{array}$

Calculation:

The given system of equations:

  $\begin{array}{l}6c+5d=7\\ 3c-10d=-4\end{array}$

By using the following steps to find the determinant for the given matrix, using the Cramer’s rule are as shown below:

  $\begin{array}{l}x=\frac{\left|\begin{array}{cc}m& b\\ n& g\end{array}\right|}{\left|C\right|}\text{ , }y=\frac{\left|\begin{array}{cc}a& m\\ f& n\end{array}\right|}{\left|C\right|}\text{ [Use the Cramer's rule]}\\ x=\frac{\left|\begin{array}{cc}7& 5\\ -4& -10\end{array}\right|}{\left|\begin{array}{cc}6& 5\\ 3& -10\end{array}\right|}\text{ , }y=\frac{\left|\begin{array}{cc}6& 7\\ 3& -4\end{array}\right|}{\left|\begin{array}{cc}6& 5\\ 3& -10\end{array}\right|}\text{ [Substitue the values from the given equations]}\\ x\text{=}\frac{(7)(-10)-(5)(-4)}{(6)(-10)-(5)(3)}\text{ , }y=\frac{(6)(-4)-(7)(3)}{(6)(-10)-(5)(3)}\text{ [Write the diagonal of each element]}\\ x=\frac{-70+20}{-60-15}\text{ , }y=\frac{-24-21}{-60-15}\text{ [Multiply]}\end{array}$

  $\begin{array}{l}x=\frac{-50}{-75}\text{ , }y=\frac{-45}{-75}\text{ [Subtract]}\\ x=0.67\text{ , }y=0.6\end{array}$

Therefore, the solution of the system of equation is $(0.67,0.6)$ .