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3x – 2y = \[\frac{5}{2}\] ; \[\frac{1}{3}x + 3y = - \frac{4}{3}\]\[D = \begin{vmatrix}3 & - 2 \\ \frac{1}{3} & 3\end{vmatrix} = 9 + \frac{2}{3} = \frac{29}{3}\]
\[ D_x = \begin{vmatrix}\frac{5}{2} & - 2 \\ \frac{- 4}{3} & 3\end{vmatrix} = \frac{15}{2} - \frac{8}{3} = \frac{29}{6}\]
\[ D_y = \begin{vmatrix}3 & \frac{5}{2} \\ \frac{1}{3} & \frac{- 4}{3}\end{vmatrix} = - 4 - \frac{5}{6} = \frac{- 29}{6}\]
\[x = \frac{D_x}{D} = \frac{\frac{29}{6}}{\frac{29}{3}} = \frac{1}{2}\]
\[y = \frac{D_y}{D} = \frac{\frac{- 29}{6}}{\frac{29}{3}} = \frac{- 1}{2}\]
\[\left[ x, y \right] = \left[ \frac{1}{2}, \frac{- 1}{2} \right]\]
What is Cramer's rule in math?
Cramer's rule is one of the important methods applied to solve a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
How does Cramer's rule work?
Cramer's Rule is a method that uses determinants to solve systems of equations that have the same number of equations as variables. Consider a system of two linear equations in two variables. If we are solving for x, the x column is replaced with the constant column.