# How do you solve the following system using Cramer's rule 2x-y=3, 4x-3y=5?

Jan 6, 2018

$P = \left\{\left(2 , 1\right)\right\}$

#### Explanation:

$A = \left(\begin{matrix}2 & - 1 & | & 3 \\ 4 & - 3 & | & 5\end{matrix}\right)$

$D = \det A = | \left[2 , - 1\right] , \left[4 , - 3\right] | = 2 \times \left(- 3\right) - \left(- 1\right) \times 4 = - 6 + 4 = - 2$

${D}_{1} = | \left[3 , - 1\right] , \left[5 , - 3\right] | = 3 \times \left(- 3\right) - \left(- 1\right) \times 5 = - 9 + 5 = - 4$

${D}_{2} = | \left[2 , 3\right] , \left[4 , 5\right] | = 2 \times 5 - 3 \times 4 = 10 - 12 = - 2$

$x = {D}_{1} / D = \frac{- 4}{-} 2 = 2$

$y = {D}_{2} / D = \frac{- 2}{-} 2 = 1$

$P = \left\{\left(2 , 1\right)\right\}$