Question

Find $D_x$ for the following simultaneous equations: $3x+4y=8,x-2y=5$

Answer 1

In cramer's rule of $a_{1}x+b_{1}y=c_1,a_{2}x+b_{2}y=c_2$

$x=\frac{D_x}{D}=\frac{\left|\begin{array}{cc}{c}_1& b_1\\ c_2& b_2\end{array}\right|}{\left|\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\end{array}\right|}$

$y=\frac{D_y}{D}=\frac{\left|\begin{array}{cc}{a}_1& c_1\\ a_2& c_2\end{array}\right|}{\left|\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\end{array}\right|}$

$D_x=\left|\begin{array}{cc}{c}_1& b_1\\ c_2& b_2\end{array}\right|$

So here $D_x=\left|\begin{array}{cc}8& 4\\ 5& -2\end{array}\right|=-36$