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What are the solutions of the system? y equals x squared plus 4 x plus 3 y equals negative 2 x minus 2 a (–5, 8) and (1, –4) b (–5, 8) and (–1, 0) c (–5, 0) and (–1, 8) d no solution

User Armaghast
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Answer: b. (-5, 8) and (-1, 0)

Step-by-step explanation:

To find the solutions of the system, we can set the two equations equal to each other.

So, we have: x^2 + 4x + 3 = -2x - 2

Rearranging and combining like terms: x^2 + 6x + 5 = 0

Now we can solve for x by factoring the quadratic equation: (x + 5)(x + 1) = 0

Setting each factor equal to zero: x + 5 = 0 --> x = -5 x + 1 = 0 --> x = -1

So, the solutions for x are x = -5 and x = -1.

To find the corresponding y-values, we can substitute these x-values into one of the original equations. Let's use y = x^2 + 4x + 3.

When x = -5: y = (-5)^2 + 4(-5) + 3 y = 25 - 20 + 3 y = 8

When x = -1: y = (-1)^2 + 4(-1) + 3 y = 1 - 4 + 3 y = 0

Therefore, the solutions for the system are (-5, 8) and (-1, 0), which matches with option b. So, the correct answer is:

b. (-5, 8) and (-1, 0)

User Missmonkee
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