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# 5+y+(3x-7)i=9-3i

find x and y in the equation make it true

Alright so we are looking for what 'x=' and 'y=', so if we get them alone on one side of the equal sign it will tell us.
We can start singling out either variable but I happen to have chosen 'y' because it looks easier.

Subtract 5 from each side to make our equation: 'y+(3x-7)i=9-3i-5'

At this point I would distribute the 'i' via the distributive property and then move those two terms to the other side, making: 'y=9-3i-5-3xi+7i'

After some simple computation you can reduce to get '[]xi+[]i' and factor the 'i' out to get your 'y='.

When you have 'y=', plug that back in the place of 'y' and solve it out for 'x'. Example; '5+[]+(3x-7)i=9-3i'.
Then you should get both a 'x' and 'y' value, remember to check your work by plugging them back in.

Richard  -

You cannot solve an equation with two variables if you have only one equation; therefore, your method does not work with a single equation. (It would if we had two equations...)

Following through with your example, you get y=4 + 4i -3xi

Plugging that back in for y, you get

5 + (4 + 4i - 3xi) + (3x-7)i = 9-3i

or

9 + 4i - 3xi + 3xi-7i = 9-3i

Collecting like terms on the left, you get

9 - 3i = 9 - 3i or, further simplifying,

0 = 0

Which still leaves us without a value for x.