Lesson 4-1 Solving linear system of equations by graphing

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Presentation transcript:

Lesson 4-1 Solving linear system of equations by graphing Objective: Determine if an ordered pair is a solution to the system Solve the system by graphing

Vocabulary A system of linear equations consists of two or more linear equations. A solution of a system of two equations in two variables is an ordered pair of numbers that is a solution of both equations in the system.

Determine if solution Tell whether the ordered pair is a solution of the given system. x + 3y = 4 (–2, 2); (5, 2); –x + y = 2 3x – y = 13

Determine if solution Tell whether the ordered pair is a solution of the given system. (1, 3); 2x + y = 5 –2x + y = 1 (–3, 1);

Solving by Graphing All solutions of a linear equation are on its graph. To find a solution of a system of linear equations, you need a point that each line has in common. In other words, you need their point of intersection. y = 2x – 1 y = –x + 5

Solve by Graphing Solve the system by graphing. Check your answer. y = x y = –2x – 3

Solve by Graphing Solve the system by graphing. Check your answer. y = x – 6 y + x = –1

Solve by Graphing Solve the system by graphing. Check your answer. y = –2x – 1 y = x + 5

Solve by Graphing Solve the system by graphing. Check your answer. 2x + y = 4

Solve by Graphing Solve the system by graphing.

Solve by Graphing Solve the system by graphing.

Vocabulary Independent System – a system that has a unique solution Dependent System – a system that does not have a unique solution Inconsistent System – is a system that has no solution

Solve by Graphing Solve the system by graphing.

Solve by Graphing Solve the system by graphing.

Solve by Graphing Solve the system by graphing.

Solve by Graphing Solve the system by graphing.