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mac1147_lecture14_1_c

# mac1147_lecture14_1_c - L14 Systems of Equations A system...

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143 L14 Systems of Equations A system of equations is a set of two or more equations, each containing one or more variables. The solution set of a system of two equations in two variables is the set of all ordered pairs (, ) x y that satisfy both equations. Geometrically, they are points of intersection of the graphs of the equations. Thus, the solution set of the system of two equations in two variables is the set of all points of intersection of their graphs, if any. If a system has at least one solution, it is called consistent ; otherwise, it is called inconsistent .

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144 Systems of Linear Equations in Two Variables A system of two linear equations in two variables represents two lines. There are three possibilities : 1. The lines intersect at one point – one solution; the system is consistent and the equations are called independent . 2. The lines are coincident – infinitely many solutions; the system is consistent and the equations are called dependent .
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mac1147_lecture14_1_c - L14 Systems of Equations A system...

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