Solve the following simultaneous equations using Cramer’s rule. 2… - Vidyadip

Question

Solve the following simultaneous equations using Cramer’s rule.
$2 x+3 y=2 ; x-\frac{y}{2}=\frac{1}{2}$

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Answer

$\begin{aligned} & 2 x+3 y=2 \\ & x-\frac{y}{2}=\frac{1}{2} \Rightarrow 2 x-y=1 \\ & D=\left[\begin{array}{cc}2 & 3 \\ 2 & -1\end{array}\right]=(2 \times-1)-(3 \times 2)=-2-6=-8 \\ & D_x=\left[\begin{array}{cc}2 & 3 \\ 1 & -1\end{array}\right]=(2 \times-1)-(3 \times 1)=-2-3=-5 \\ & D_y=\left[\begin{array}{ll}2 & 2 \\ 2 & 1\end{array}\right]=(2 \times 1)-(2 \times 2)=2-4=(-2) \\ & x=\frac{D_x}{D}=\frac{-5}{-8}=\frac{5}{8} y=\frac{D_y}{D}=\frac{-2}{-8}=\frac{1}{4} \\ & \therefore(x, y)=\left(\frac{5}{8}, \frac{1}{4}\right) \text { is solution. }\end{aligned}$

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