Find the value of Dx, for solving the simultaneous equations 3x + 4y = 8; x – 2y = 5 by Cramer’s rule.

[tex]\underline{\textsf{Given:}} [/tex]

[tex]\mathsf{3x+4y=8}[/tex]

[tex]\mathsf{x-2y=5}[/tex]

[tex]\underline{\textsf{To find:}} [/tex]

[tex]\textsf{Solution of the simultaneous equations by Cramer’s rule}[/tex]

[tex]\underline{\textsf{Solution:}} [/tex]

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

[tex]\mathsf{\triangle=-6-4=-10}[/tex]

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

[tex]\mathsf{{\triangle}x=-16-20=-36}[/tex]

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

[tex]\mathsf{{\triangle}y=15-8=7}[/tex]

[tex]\textsf{By Cramer’s rule}[/tex]

[tex]\mathsf{x=\dfrac{{\triangle}x}{\traingle}=\dfrac{-36}{-10}=\dfrac{36}{10}}[/tex]

[tex]\mathsf{y=\dfrac{{\triangle}y}{\traingle}=\dfrac{7}{-10}=\dfrac{-7}{10}}[/tex]

[tex]\underline{\textsf{Answer:}} [/tex]

[tex]\textsf{The solution is}[/tex]

[tex]\mathsf{x=\dfrac{36}{10}\;\;\&\;\;y=\dfrac{-7}{10}}[/tex]

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Find the value of Dx, for solving the simultaneous equations 3x + 4y = 8; x – 2y = 5 by Cramer’s rule.​