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I am told to solve the following system:

y = 2x^2 + 5x + 9

y = -4x + 5

Thank you for your time!

The y = 2x^2 + 5x + 9 factors.

Since 2 is prime, try (2x+ )(x+ ).

Since the 9 is 3*3, try (2x+3)(x+3).

Sure enough, multiplying the right side on the equation y = (2x+3)(x+3)

gives y = 2x^2 + 5x + 9.

Assuming we are trying to get y = 0, we need to have either 2x+3 = 0 or x+3 = 0.

Subtracting 3 from both sides on both equations gives 2x = -3 and x = -3.

The 2nd equation is solved already, for it is just x=-3.

The 1st equation needs to be divided by 2 on both sides.

That gives x = -3/2. This is the same as x = -1½.

Algebra

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