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System of Two Linear Equations in Two Variables

This content covers the fundamental concepts of systems of linear equations and inequalities in two and three variables. It explains the standard forms of equations, methods for solving including the Substitution and Linear Combination methods, and the significance of ordered pairs and triples. Detailed definitions are provided for concepts such as solutions of systems, linear equations, and functions of two variables. This comprehensive guide serves as a valuable resource for anyone looking to grasp these essential mathematical concepts.

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System of Two Linear Equations in Two Variables

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  1. System of Two Linear Equations in Two Variables • Two equations of the form Ax + By = C and Dx + Ey = F where x and y are both variables.

  2. Solution of a system of linear equations • An ordered pair (x, y) that satisfies each equation of the system.

  3. Substitution Method • The method for solving a system of equations where a scale factor is used.

  4. Linear Combination Method • The method for solving a system of equations where a variable is isolated

  5. Solution of a system of linear inequalities • An ordered pair that is a solution of each inequality in the system

  6. Ordered triple • A set of three numbers of the form (x, y, z) that represents a point in space.

  7. Linear equation in three variables • An equation of the form ax +by + cz where x, y, and z are variables.

  8. Function of two variables • a system made up of three linear equations in three variables

  9. System of three linear equations in three variables • A relation with exactly one output for each input.

  10. Solution of a system of three linear equations • An ordered triple (x, y, z) that is a solution of all three equations of the system.

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