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If $3 x+i(4 x-y)=6-i$ where $x$ and $y$ are real numbers, then the values of $x$ and $y$ are respectively,
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Verified Answer
The correct answer is:
2, 9
$3 x+i(4 x-y)=6-i$
On comparing real and imaginary parts of LHS and RHS, we get
$$
\begin{aligned}
& 3 x=6 \text { and } 4 x-y=-1 \\
& \Rightarrow \quad 3 x=6 \Rightarrow x=2 \\
& \text { Put } x=2 \text { into } 4 x-y=-1 \text {, we get } \\
& 4 \times 2-y=-1 \\
& \Rightarrow \quad 8+1=y \Rightarrow y=9 \\
&
\end{aligned}
$$
On comparing real and imaginary parts of LHS and RHS, we get
$$
\begin{aligned}
& 3 x=6 \text { and } 4 x-y=-1 \\
& \Rightarrow \quad 3 x=6 \Rightarrow x=2 \\
& \text { Put } x=2 \text { into } 4 x-y=-1 \text {, we get } \\
& 4 \times 2-y=-1 \\
& \Rightarrow \quad 8+1=y \Rightarrow y=9 \\
&
\end{aligned}
$$
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