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Solving Simultaneous Linear Equation Using Cramer's Rule

Write Dx fo...

Question

Write $D_{x}$ for the following simultaneous equations :
$3 x + 4 y = 8; x - 2 y = 5$

A

D_{x} = ∣ ∣ ∣ \begin{matrix} 6 & 4 5 & - 5 \end{matrix} ∣ ∣ ∣

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B

D_{x} = ∣ ∣ ∣ \begin{matrix} 8 & 4 5 & - 2 \end{matrix} ∣ ∣ ∣

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C

D_{x} = ∣ ∣ ∣ \begin{matrix} 2 & 6 9 & - 2 \end{matrix} ∣ ∣ ∣

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D

D_{x} = ∣ ∣ ∣ \begin{matrix} 9 & 1 16 & - 1 \end{matrix} ∣ ∣ ∣

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Solution

The correct option is C $D_{x} = ∣ ∣ ∣ \begin{matrix} 8 & 4 5 & - 2 \end{matrix} ∣ ∣ ∣$
$D_{x}$ of two simulataenous linear equations $a_{1} x + b_{1} y = c_{1}$ and $a_{2} x + b_{2} y = c_{2}$
is given by $∣ ∣ ∣ \begin{matrix} c_{1} & b_{1} c_{2} & b_{2} \end{matrix} ∣ ∣ ∣$
Hence, for the given equations, $D_{x} = ∣ ∣ ∣ \begin{matrix} 8 & 4 5 & - 2 \end{matrix} ∣ ∣ ∣$

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Similar questions

State the following statement is true or false

3 x + 4 y = 8; x - 2 y = 5

D_{x} = ∣ ∣ ∣ \begin{matrix} 8 & 4 5 & - 2 \end{matrix} ∣ ∣ ∣

Q. Write D_x for the following simultaneous equations :
(i) 3x + 4y = 8 ; x

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