Question

solve by cremers method- x+4y=3 and 2x+9y=5​

Answer 1

Given:

$-x +4y = 3\\\\2x+ 9y = 5$

To prove:

Solve cramer's method

Solution:

Rule:

$\bold {ax+by=e} \\ \bold{ cx+dy = f}$

$\bold { \[x = \frac{{\left| {\begin{array}{*{20}{c}}e&b\\f&d\end{array}} \right|}}{{\left| {\begin{array}{*{20}{c}}a&b\\c&d \end{array}} \right|}}\]}$

$\bold{\[y= \frac{{\left| {\begin{array}{*{20}{c}}a&e\\c&f\end{array}} \right|}}{{\left| {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right|}}\] }$

Find the value:

$\rightarrow -x + 4y = 3\\\rightarrow 2x+9y =5\\\\ \rightarrow \[\ x = \frac{{\left| {\begin{array}{*{20}{c}}3&4\\5&9\end{array}} \right|}}{{\left| {\begin{array}{*{20}{c}}-1&4\\2&9 \end{array}} \right|}}\]$

$\rightarrow \[x = \frac{27-20}{-9-8} \]\\\\\rightarrow \[x = \frac{7}{-17} \]$

$\rightarrow x= \frac{-7}{17}$

$\rightarrow \bold { \[y = \frac{{\left| {\begin{array}{*{20}{c}}-1&3\\2&5\end{array}} \right|}}{{\left| {\begin{array}{*{20}{c}}-1&4\\2&9 \end{array}} \right|}}\]}$

$\rightarrow \ y= \frac{-5 - 6}{-9 - 8}\\\\\rightarrow \ y= \frac{-11}{-17}\\\\\rightarrow \ y= \frac{11}{17}$

The final value of x and y  are "-7/17" and "11/17" respectively.