SOLUTION: how do you solve, step by step,: x(2+6i)+y(3+8i)=-6-14i?

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Question 186670: how do you solve, step by step,: x(2+6i)+y(3+8i)=-6-14i?
Found 3 solutions by jim_thompson5910, vleith, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%282%2B6i%29%2By%283%2B8i%29=-6-14i Start with the given equation.


2x%2B6xi%2B3y%2B8yi=-6-14i Distribute


%282x%2B3y%29%2B%286x%2B8y%29i=-6-14i Rearrange and group like terms.


This means that

2x%2B3y=-6 (this is the real part)

and

6x%2B8y=-14 (this is the imaginary part)



So all that you have to do is solve the system



system%282x%2B3y=-6%2C6x%2B8y=-14%29


to find 'x' and 'y'

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
+x%282%2B6i%29%2By%283%2B8i%29=-6-14i
2x+%2B+6xi+%2B+3y+%2B+8yi+=+-6+-+14i
2x%2B3y+%2B+i%286x%2B8y%29+=+-6+-+14i
So
2x+%2B+3y+=+-6
6x+%2B+8y+=+-14
now solve this set of linear equations. I am guessing you know how to do this. I would use elimination.
If you don't know how, send an email and I'll work it for you

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
how do you solve, step by step,: 

When there are both real and imaginary terms
in an equation, 

1. the sum of all the real terms (those which
do not contain an "i", on the left is equal to 
the sum of all the real terms on the right, 

and 

2. all the imaginary terms (those containing "i")  
on the left is equal to the sum of all the
imaginary terms on the right.


x%282%2B6i%29%2By%283%2B8i%29=-6-14i

First we remove the parentheses using the 

2x%2B6xi%2B3y%2B8yi=-6-14i

Write the equation leaving out the terms which
DO NOT contain "i":

2x%2B3y=-6

That's one equation:

Now do just the revers, write the equation this 
time leaving out the terms which DO contain "i":

6xi%2B8yi=-14i

Now divide every term by i:

6x%2B8y=-14

So now we have this system:

system%282x%2B3y=-6%2C6x%2B8y=-14%29

Solve that system and get x=3 and y=-4

Edwin