Final answer:
To solve the system of equations, substitute the value of y from the first equation into the second equation and solve for x. Then substitute the value of x back into the first equation to find the corresponding value of y.
Step-by-step explanation:
To solve the system of equations algebraically, we can substitute the value of y from the first equation into the second equation, since they both equal to y. So, we have: -x^2 - 3x + 3 = 3x + 3. Combining like terms, we get: -x^2 - 6x = 0. Factoring out x, we get: x(-x - 6) = 0. Solving for x, we find that x = 0 or x = -6. Substituting these values back into the first equation, we find that corresponding values of y are y = 3 and y = -15, respectively. Therefore, the system of equations has two solutions: (0, 3) and (-6, -15).
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