Solving Linear Systems

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Presentation transcript:

Solving Linear Systems Section 1.4

What You Will Learn Visualize solutions of systems of linear equations in three variables. Solve systems of linear equations in three variables algebraically. Solve real-life problems.

Visualizing Solutions of Systems A linear equation in three variables (Take Note) x, y, and z is an equation of the form ax + by + cz = d, where a, b, and c are not all zero.

The graph of a linear equation in three variables is a plane in three-dimensional space. The graphs of three such equations that form a system are three planes whose intersection determines the number of solutions of the system, as shown in the diagrams below.

(Take Note)

solve the system using the elimination method.

solve the system of linear equations using the substitution method.