Complex number

sharks

The problem statement, all variables and given/known data
Given that the real and imaginary parts of the complex number [itex]z=x+iy[/itex] satisfy the equation [itex](2-i)x-(1+3i)y=7[/itex]. Find x and y.

The attempt at a solution
I know it's quite simple. Just equate the real and imaginary parts, but i checked and redid it again, but the answer still evades me!
[tex](2x-y-7) + i(-x-3y)=0
\\2x-y-7=x
\\x-y=7\, (1)
\\-x-3y=y
\\4y+x=0\, (2)
\\x=28/5
\\y=-7/5
[/tex]
I replaced in the original equation but i can't get 7 on the L.H.S.
The correct answers: x=3 and y=-1.

LCKurtz

Why aren't those 0 on the right side?

SammyS

When you write:

[itex]2x-y-7=x[/itex]

and

[itex]-x-3y=y\ ,[/itex]

you are saying that

[itex](2x-y-7) + i(-x-3y)=z\ .[/itex]

That's not what you're trying to solve !

sharks

I was confused about z=x+iy. I thought i had to compare the real and imaginary parts of z with those of the equation in order to solve it. I now realize that it has absolutely nothing to do with z. All i had to do was solve the equation independently and ignore whatever was given for z.

Solving:[tex]2x-y=7
\\-x-3y=0[/tex]I get the correct answers.

Thank you, LCKurtz and SammyS.