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Algebra/Algebra systems (12.7-3)


Solve the following system via elimination:
y = x^2 + 2
-4x - y = 10

Thank you!

Take y and put it in the second equation.
This gives -4x - x - 2 = 10.
Subtracting 10 from both sides gives -4x - x - 2 = 10.
Rearranging terms and subtracting 10 from both sides gives -x - 4x - 12 = 0.
Multiplying through by -1 gives x + 4x + 12 = 0.

Since the square-root in the quadratic equation has b-4ac,
and a=1, b=4, and c=12, this can be seen to give 16-48 = -32.

Have you dealt with the square-root of negative numbers?
If not, that is undefined.

If, on the other hand, you've dealt with them,
that gives a complex number as the answer for x.
Later in algebra, if you're not there yet, they define the square-root of -1.

As I said, if you haven't dealt with the square-root of negative numbers,
there is no solution.


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Scott A Wilson


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