Question

Find the value of Dx, for solving the simultaneous equations

3x + 4y = 8; x – 2y = 5 by Cramer’s rule.​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{3x+4y=8}$

$\mathsf{x-2y=5}$

$\underline{\textsf{To find:}}$

$\textsf{Solution of the simultaneous equations by Cramer's rule}$

$\underline{\textsf{Solution:}}$

$\begin{gathered}\mathsf{\triangle=\left|\begin{array}{cc}3&4\\1&-2\end{array}\right|}\end{gathered}$

$\mathsf{\triangle=-6-4=-10}$

$\begin{gathered}\mathsf{{\triangle}x=\left|\begin{array}{cc}8&4\\5&-2\end{array}\right|}\end{gathered}$

$\mathsf{{\triangle}x=-16-20=-36}$

$\begin{gathered}\mathsf{{\triangle}y=\left|\begin{array}{cc}3&8\\1&5\end{array}\right|}\end{gathered}$

$\mathsf{{\triangle}y=15-8=7}$

$\textsf{By Cramer's rule}$

$\mathsf{x=\dfrac{{\triangle}x}{\traingle}=\dfrac{-36}{-10}=\dfrac{36}{10}}$

$\mathsf{y=\dfrac{{\triangle}y}{\traingle}=\dfrac{7}{-10}=\dfrac{-7}{10}}$

$\underline{\textsf{Answer:}}$

$\textsf{The solution is}$

$\mathsf{x=\dfrac{36}{10}\;\;\&\;\;y=\dfrac{-7}{10}}$

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