Final answer:
To determine the value of a variable, the approach varies with the problem: use substitution, elimination, or graphing for systems of equations; the quadratic formula for quadratic equations; matrix multiplication for complex systems; and inverse functions for solving inverses.
Step-by-step explanation:
To find the value of each variable, different mathematical methods are used depending on the type of problem:
- Systems of equations: To solve a system of linear equations, you can use methods such as substitution, elimination, or graphing. The goal is to find the values of the variables that satisfy all equations simultaneously.
- Quadratic formula: To solve a quadratic equation of the form ax^2 + bx + c = 0, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). This formula will provide the solutions for the variable x.
- Matrix multiplication: This is used when dealing with systems of equations that can be represented in matrix form. Multiplying matrices can help simplify complex systems and make it easier to solve for the unknown variables.
- Inverse functions: To find the original value before a function was applied, you use the inverse of that function. This requires that the function have an inverse, which is not the case for all functions.
To apply these methods, explicitly list all known values, identify what needs to be solved, and then select the appropriate method to find the mentioned correct answer in the final answer.