Question

9x + 5y = 10
3y − 2x = 8

Answer 1

\[\text{ Given }: 9x + 5y = 10 \] 
\[ 3y - 2x = 8 \] 
Rearranging the second equation, the two equations can be written as 
\[ 9x + 5y = 10\] 
\[ - 2x + 3y = 8\] 
Now, 
\[D = \begin{vmatrix} 9 & 5\\ - 2 & 3 \end{vmatrix} = 27 + 10 = 37\] 
\[ D_1 = \begin{vmatrix} 10 & 5\\ 8 & 3 \end{vmatrix} = 30 - 40 = - 10\] 
\[ D_2 = \begin{vmatrix} 9 & 10 \\ - 2 & 8 \end{vmatrix} = 72 + 20 = 92\] 
Using Cramer's rule, we get
\[x = \frac{D_1}{D} = \frac{- 10}{37}\] 
\[y = \frac{D_2}{D} = \frac{92}{37}\] 
\[ \therefore x = \frac{- 10}{37}\text{ and }y = \frac{92}{37}\]