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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 - x² - 2 = 10.

Subtracting 10 from both sides gives -4x - x² - 2 = 10.

Rearranging terms and subtracting 10 from both sides gives -x² - 4x - 12 = 0.

Multiplying through by -1 gives x² + 4x + 12 = 0.

Since the square-root in the quadratic equation has b²-4ac,

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.

Algebra

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