Solve the system of equations algebraically. The system is given by and . Find the value of that satisfies both equations.
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's ability to solve a system of linear and quadratic equations algebraically. The key steps involve substituting the linear equation into the quadratic equation, simplifying, and solving the resulting quadratic equation.
Key Concept Explanation
The substitution method involves expressing one variable from one equation and substituting it into the other. This eliminates one variable and forms a single equation in the remaining variable, which can be solved using standard algebraic techniques.
Step-by-step Solution
1. Substitute into the quadratic equation :
2.
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