Solve the following simultaneous equations using Cramer's rule.
$y = \frac{5 x - 10}{2}; 4 x + 5 = - y$

x = 0; y = - 5

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x = 1; y = - 4

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x = 3; y = - 4

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x = 0; y = - 2

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Solution

The correct option is B $x = 0; y = - 5$
Given equations are
$5 x - 2 y = 10 4 x + y = - 5$
We have $D = ∣ ∣ ∣ \begin{matrix} 5 & - 2 4 & 1 \end{matrix} ∣ ∣ ∣ = 5 d - (- 8) = 13$
Thus $D_{x} = ∣ ∣ ∣ \begin{matrix} 10 & - 2 - 5 & 1 \end{matrix} ∣ ∣ ∣ = 10 - (- 10) = 0$
and $D_{y} = ∣ ∣ ∣ \begin{matrix} 5 & 10 4 & - 5 \end{matrix} ∣ ∣ ∣ = - 25 - 40 = - 65$
Therefore, $x = \frac{D_{x}}{D} = \frac{0}{13} = 0$
and $y = \frac{D_{y}}{D} = \frac{- 65}{13} = - 5$

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