1140 L19 - Lecture 19: Sections 7.1 and 7.2 System of...

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Lecture 19: Sections 7.1 and 7.2 System of Equations Def. A system of equations is a collection of two or more equations, each containing one or more variables. Def. A system of the following form ( a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 is a system of two linear equations in two variables . The solution set of the system is all ordered pairs ( x; y ) that satisfy both equaitons.
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Solving by Graphing ex. Solve each system: 1) ± x + 2 y = 4 x ± y = 1 2) ± x ± y = ± 1 ± 2 x + 2 y = 2 3) ± x + y = 3 x + y = ± 2 There are 3 possibilities: 1. The lines intersect at one point. The system has exactly one solution . 2. The lines coincide . There are in±nitely many solutions (every point on the line). 3. The lines are parallel . The system has no solutions . To solve a system of equations is to ±nd the intersecting point(s) of the equations.
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The Method of Substitution 1. Solve for one variable in an equation in terms of the other. 2.
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L19 - Lecture 19: Sections 7.1 and 7.2 System of...

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