Question

(x+y)-(3x+2y)i=5+2i​

Answer 1

Correct Question:

$\sf{(x+y)-(3x+2y)i=5+2i, \ find \ the \ value}$

$\sf{of \ x \ and \ y.}$

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Answer:

$\sf{The \ values \ of \ x \ and \ y \ are \ -12 \ and \ 17}$

$\sf{respectively. }$

Given:

$\sf{(x+y)-(3x+2y)i=5+2i}$

To find:

$\sf{The \ values \ of \ x \ and \ y.}$

Solution:

$\sf{(x+y)-(3x+2y)i=5+2i}$

$\sf{On \ equating \ real \ and \ imaginary \ parts}$

$\sf{we \ get,}$

$\sf{x+y=5...(1)}$

$\sf{-(3x+2y)=2}$

$\sf{\therefore{3x+2y=-2...(2)}}$

$\sf{Multiply \ equation(1) \ by \ 2, \ we \ get}$

$\sf{2x+2y=10...(3)}$

$\sf{Subtract \ equation(3) \ from \ equation(2), \ we \ get}$

$\sf{3x+2y=-2}$

$\sf{-}$

$\sf{2x+2y=10}$

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$\boxed{\sf{x=-12}}$

$\sf{Substitute \ x=-12 \ in \ equation(1), \ we \ get}$

$\sf{-12+y=5}$

$\boxed{\sf{\therefore{y=17}}}$

$\sf\purple{\tt{\therefore{The \ values \ of \ x \ and \ y \ are \ -12 \ and \ 17}}}$

$\sf\purple{\tt{respectively. }}$