SOLUTION: Find the values of x and y for which the complex numbers (2x+3y)+i(2y-1) and 10+i(5-x) are equal.

Question 1029385: Find the values of x and y for which the complex numbers
(2x+3y)+i(2y-1) and 10+i(5-x) are equal.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Find the values of x and y for which the complex numbers
(2x+3y)+i(2y-1) and 10+i(5-x) are equal.
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Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

It gives you two equations

2x + 3y = 10,    (1)
2y-1    = 5-x.   (2)

From (2), express x = 5 - 2y + 1 = 6 - 2y  and substitute it into (1). You will get 

2*(6-2y) + 3y = 10,

12 - 4y + 3y = 10,

-y = 10 - 12,

-y = -2,

y = 2.

Then x = 6 - 2y = 6 - 2*2 = 6 - 4 = 2.

Answer.  x = 2,  y = 2.

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