Question:
Solve for $x:(1-i) x+(1+i) y=1-3 i$
Solution:
We have, $(1-\mathrm{i}) \mathrm{x}+(1+\mathrm{i}) \mathrm{y}=1-3 \mathrm{i}$
$\Rightarrow x-i x+y+i y=1-3 i$
$\Rightarrow(x+y)+i(-x+y)=1-3 i$
On equating the real and imaginary coefficients we get,
$\Rightarrow x+y=1$ (i) and $-x+y=-3$ (ii)
From (i) we get
$x=1-y$
Substituting the value of x in (ii), we get
$-(1-y)+y=-3$
$\Rightarrow-1+y+y=-3$
$\Rightarrow 2 y=-3+1$
$\Rightarrow y=-1$
$\Rightarrow x=1-y=1-(-1)=2$
Hence, $x=2$ and $y=-1$
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