Final answer:
To solve the system of equations algebraically, use the method of substitution. The solutions to this system are (-4, -18) and (5, 15).
Step-by-step explanation:
To solve the system of equations algebraically, we can use the method of substitution. First, solve one equation for y and substitute it into the other equation. Let's start with the first equation: y - 10 = 11x + x². Rearrange the equation to solve for y: y = 11x + x² + 10. Now, substitute this expression for y in the second equation: (11x + x² + 10) - 12x = 30. Simplify and rearrange: x² - x - 20 = 0. Factoring or using the quadratic formula, we find two possible solutions for x: x = -4 or x = 5. Substituting these values back into the expressions for y, we get two solutions for the system: (-4, -18) and (5, 15).
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