Final answer:
To solve the system of equations algebraically, substitute y from the first equation into the second equation to get a quadratic equation. Solve the quadratic equation to find the values of x. Substitute these values into the first equation to find the corresponding values of y. The solution to the system of equations is the set of ordered pairs (x, 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.
Substituting 3x + 3 for y in the second equation gives us:
3x + 3 = -x² - 3x + 3
Rearranging the equation gives us a quadratic equation:
x² + 6x = 0
Solving this quadratic equation, we find two possible values for x: x = 0 and x = -6.
Substituting these values of x into the first equation, we can find the corresponding values of y: y = 3(0) + 3 = 3 and y = 3(-6) + 3 = -15.
Therefore, the solution to the system of equations is (0, 3) and (-6, -15).
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