Section 10.1: Systems of Linear Equations in Two Variables

1. State what it means to find a solution to a system of equations, and what it means to solve a system of equations.
2. State types of solutions that a system of linear equations in two variables can have, and sketch a graph demonstrating each type of solution.
3. Identify when a system of linear equations in two variables has no solution, one solution, or infinitely many solutions.
4. State the operations that can be performed to a system of linear equations that results in an equivalent system of linear equations.
5. Solve a system of linear equations in two variables using each of the
   • substitution method
   • elimination method
   • graphical method
6. Given a ‘word problem’ that can modeled using a system of linear equations in two variables:
   • Identify the variables in the problem.
   • Express all unknown quantities in terms of the variables.
   • Set up a system of equations.
   • Solve the system of equations and interpret the results.

Section 10.2: Systems of Linear Equations in Several Variables

1. Distinguish between systems of linear and nonlinear equations.
2. Solve a system of linear equations in triangular form using back-substitution.
3. Solve a system of linear equations in several variables using Gaussian elimination and back-substitution.
4. Identify when a system of linear equations in several variables has no solution, one solution, or infinitely many solutions.
5. Set up a system of linear equations to balance a given chemical reaction, and interpret the solution to the system of linear equations in terms of the coefficients of the balanced chemical reaction.