Chapter 4.5, Problem 14CYU

To determine

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

Answer to Problem 14CYU

The solution of the system is (2,5).

Explanation of Solution

Given,

The set of equation is given as,

  $\begin{array}{l}5x+6y=20\\ -3x-7y=-29\end{array}$

Calculation:

Calculate the value of x using Cramer’s rule.

  $\begin{array}{c}x=\frac{\left|\begin{array}{cc}20& 6\\ -29& -7\end{array}\right|}{\left|\begin{array}{cc}5& 6\\ -3& -7\end{array}\right|}\\ =\frac{20\left(-7\right)-\left(-29\right)\left(6\right)}{5\left(-7\right)-\left(-3\right)\left(6\right)}\\ =\frac{-34}{-17}\\ =2\end{array}$

Calculate the value of y using Cramer’s rule.

  $\begin{array}{c}y=\frac{\left|\begin{array}{cc}5& 20\\ -3& 29\end{array}\right|}{\left|\begin{array}{cc}5& 6\\ -3& -7\end{array}\right|}\\ =\frac{5\left(-29\right)-\left(-3\right)\left(20\right)}{5\left(-7\right)-\left(-3\right)\left(6\right)}\\ =\frac{-85}{-17}\\ =5\end{array}$

Thus, the solution of the system is (2,5).