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

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 these systems include substitution, elimination, and graphical representation. 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. This concept is essential for accurately interpreting and solving related equations.

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 solutions. This visual approach can provide insights that algebraic methods may not immediately reveal.