Algebra-1

Question Analysis
This question tests the student's ability to solve a system of linear and quadratic equations algebraically. The system is given by: ,       . The goal is to find the value of that satisfies both equations.

Key Concept Explanation
To solve this system, we use the substitution method. We substitute the expression for from the linear equation into the quadratic equation, then solve the resulting quadratic equation for . After finding , we substitute back into the linear equation to find .

Step-by-step Solution
1. Substitute into :

2. Rearrange the equation to standard quadratic form:

3. Solve the quadratic equation using the quadratic formula , where , , and :



4. Find