Question

if (1+2i)x - (1-i)y=2-i, where i=√-1, then find the value of x and y​

Answer 1

Answer:

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Step-by-step explanation:

$to \: find = \\ values \: of \: x \: and \: y \\ \\ here \: \\ (1 + 2i)x - (1 - i)y = 2 - i \\ \\ = x + 2ix \: - (y - iy) \\ \\ = x + 2ix - y + iy \\ \\ = (x - y) + (2x + y)i \\ \\ comparing \: real \: and \: imaginary \: parts \\ \\ x - y = 2 \: \: \: \: \: \: \: \: (1) \\ \\ 2x + y = - 1 \: \: \: \: \: \: \: \: \: (2) \\ \\ applying \: now \\ (1) + (2) \\ \\ 3x = 1 \\ \\ x = \frac{1}{3} \\ \\ substitute \: value \: of \: x \: in \: (1) \\ we \: get \\ \\ y = \frac{ - 5}{3} \\ \\ hence \: then \\ \\ (x,y) = ( \: \frac{1}{3} \: , \: \frac{ - 5}{3} \: )$