PP Section 10.1

PP Section 10.1 - Systems of Two Linear Equations in Two...

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Systems of Two Linear Equations in Two Unknowns

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A system of equations is a collection of two or more equations, each containing one or more variables. A solution of a system of equations consists of values for the variables that reduce each equation of the system to a true statement. To solve a system of equations means to find all solutions of the system. When a system of equations has at least one solution, it is said to be consistent ; otherwise it is called inconsistent .
We will consider systems of two equations and two unknowns. Each equation in such systems represents a line, so solving the system is equivalent to finding the point(s) of intersection of the lines. There are three possibilities: The lines are parallel, so they do NOT intersect. The lines intersect at exactly one point. The equations represent the same line, so the solution of the system is infinite.

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Graphically Inconsistent system Consistent systems
There are several methods for solving systems of equations. We will consider two algebraic

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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 10.1 - Systems of Two Linear Equations in Two...

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