Question

3x-2y=5/2;1/3x+3y=-4/3 by cramer's rule

Answer 1

.... find this solution..........

Answer 2

Answer: $x=-\dfrac{1}{2},\ y=\dfrac{-1}{2}$

Step-by-step explanation:

Given system: $3x-2y=5/2\\\\1/3x+3y=-4/3$

Using Cramer rule:  

$D=\begin{vmatrix}3 & -2\\ 1/3 & 3\end{vmatrix}=\dfrac{29}{3}$

$D_1=\begin{vmatrix}5/2& -2\\ -4/3 & 3\end{vmatrix}=\dfrac{29}{6}$

$D_2=\begin{vmatrix}3 & 5/2\\ 1/3 & -4/3\end{vmatrix}=\dfrac{-29}{6}$

Now, $x=\dfrac{D_1}{D}=\dfrac{\dfrac{29}{6}}{\dfrac{29}{3}}=\dfrac{1}{2}$

$x=\dfrac{D_2}{D}=\dfrac{\dfrac{-29}{6}}{\dfrac{29}{3}}=\dfrac{-1}{2}$

Hence, $x=-\dfrac{1}{2},\ y=\dfrac{-1}{2}$