In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

Verified step by step guidance

1. Identify the piecewise function and the intervals for each piece.
2. Determine which piece of the function applies to the given input value or range.
3. For the applicable piece, write down the equation or expression that defines it.
4. Solve the equation or expression for the given input value or range.
5. Verify the solution by checking if it satisfies the conditions of the piecewise function.

Key Concepts

Systems of Equations

A system of equations consists of two or more equations with the same set of variables. The goal is to find the values of the variables that satisfy all equations simultaneously. Common methods for solving systems include substitution, elimination, and graphing. Understanding how to manipulate and solve these equations is crucial for finding solutions.

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. Each 'piece' of the function applies to a specific interval of the domain. To solve problems involving piecewise functions, one must identify which expression to use for a given input and ensure continuity and correctness across the defined intervals.

Graphical Interpretation

Graphical interpretation involves visualizing equations and functions on a coordinate plane. For systems of equations, the solution can often be found at the intersection points of the graphs. Understanding how to plot piecewise functions and systems graphically aids in comprehending their behavior and finding solutions effectively.