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Solve the following systems by substitution:
Solution:
Consider the given equations above
The first equation can be factored by the sum of the two cubes as follows
But
Hence, the above equation becomes
Substitute the value of y to the above equation, we have
By using completing the square method, the value of x is
If
, then y equals
If
, then y equals
Since the solutions of the two equations have imaginary numbers or complex numbers, then the two equations have no solution.