00:01
In this problem, we have been asked to solve for all possible values of the real numbers x and y in the given equation, which is x plus 2y plus 3 ,000, minus 1 is equal to 0.
00:15
Now, we can rewrite 0 as 0 plus 0.
00:18
Then what are the real parts of the complex numbers? we have this and this, and what are the imaginary parts? we have this and this.
00:26
Now, recall that whenever two complex numbers are equal, their real parts will be.
00:30
Equal and their imaginary parts will also be equal.
00:33
So if the real parts are equal, we have that x plus 2y plus 3 is 0.
00:37
And if we equate the imaginary parts, we have the 3x minus y minus 1 is equal to 0.
00:42
So from here we can obtain that y is equal to 3x minus 1.
00:45
And let's substitute that in this equation over here.
00:48
So we end up with x plus 2 times y, which is 3x minus 1 plus 3...