Maths · Quadratic equations in real and complex number systems and their solutions
What are the solution(s) to the system of equations and
What are the solution(s) to the system of equations \( \boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{9} \) and \( \boldsymbol{y}-\boldsymbol{3}= \) \( x ? \)
- A. -3,0 and 4,7
- B. -3,0
- C. 4,7
- D. 4,-3
Step-by-step solution
Solve the system: y = x^2 - 9 and y - 3 = x => y = x + 3. Substitute: x + 3 = x^2 - 9 => x^2 - x - 12 = 0 => (x-4)(x+3)=0 => x=4 or x=-3. Corresponding y: y=7 for x=4, y=0 for x=-3. Solutions: (-3,0) and (4,7). Option A lists both pairs.
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