Question

$6x - 3y = - 10; 3x + 5y - 8 = 0$
Solve the following simultaneous equations by Cremer's method​

Answer 1

$\LARGE\mathfrak{\underline{\underline{\: \: \: Solution :-}}}$

↦ 6x - 3y = - 10 ..( i )

↦ 3x + 5y = 8 ...( ii )

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$\large\: \bigstar\textsf{\: \: \: D = \left[\begin{array}{c c} 6 & - 5 \\ 3 & 5 \end{array}\right] }\\\\\\\large: \: \Longrightarrow\textsf{= ( 6 × 5 ) - [ 3 × ( - 3 )]}\\\\\\\large: \: \Longrightarrow\textsf{= 15 - ( - 9 )}\\\\\\\large: \: \Longrightarrow\textsf{= 15 + 9}\\\\\\\large: \: \Longrightarrow\underline{\boxed{\textsf{D = 24}}}$

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$\large\: \bigstar\textsf{\: \: \: D_{x} = \left[\begin{array}{c c} -10 & - 3 \\ 8 & 5 \end{array}\right] }\\\\\\\large: \: \Longrightarrow\textsf{= [ ( - 10 ) × 5 ] - [ 8 × ( - 3 ) ] }\\\\\\\large: \: \Longrightarrow\textsf{= ( - 50 ) - ( - 24 ) }\\\\\\\large: \: \Longrightarrow\textsf{= - 50 + 24 }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf{ D_{x} = - 26 }}}$

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$\large:\: \bigstar\textsf{\: \: \: D_{y} = \left[\begin{array}{c c} 6 & - 10 \\ 3 & 8 \end{array}\right] }\\\\\\\large: \: \Longrightarrow\textsf{= ( 6 × 8 ) - [ 3 × ( - 10 ) ]}\\\\\\\large: \: \Longrightarrow\textsf{= 48 - ( - 30 )}\\\\\\\large: \: \Longrightarrow\textsf{= 48 + 30}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf{ D_{y} = 78 }}}$

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$\large\: \bigstar\textsf{\: \: \: x = \cfrac{D_{x}}{D} }\\\\\\\large: \: \Longrightarrow\textsf{ = \cancel\cfrac{-26}{24} }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf{ x = \cfrac{- 18}{17} }}}$

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$\large\: \bigstar\textsf{\: \: \: y = \cfrac{D_{y}}{D} }\\\\\\\large: \: \Longrightarrow\textsf{ = \cancel\cfrac{78}{24} }\\\\\\\large: \: \Longrightarrow\underline{\boxed{\textsf{ x = \cfrac{39}{12} }}}$

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$\large\textbf{∴ ( x , y ) = \left( \cfrac{- 18}{17} , \cfrac{39}{12}\right) \: \: \: is \: \: \: the \: \: \: Solution}$