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L19 - Lecture 19 Sections 7.1 and 7.2 System of Equations...

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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. A solution of a system of equations consists of values of the variables that satisfy eachequation in the system. To Solve a system is to find all solutions of the system. A system is consistent if it has at least one solution; otherwise it is called inconsistent . Def. A system of the form uni007B.alt04 u1D44E 1 u1D465 + u1D44F 1 u1D466 = u1D450 1 u1D44E 2 u1D465 + u1D44F 2 u1D466 = u1D450 2 is a system of two linear equations in two variables . The solution set of the system is all ordered pairs ( u1D465,u1D466 ) that satisfy the system.
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Solving by Graphing ex. Solve each system: 1) uni007B.alt03 u1D465 + 2 u1D466 = 4 u1D465 u1D466 = 1 2) uni007B.alt03 u1D465 u1D466 = 1 2 u1D465 + 2 u1D466 = 2 3) uni007B.alt03 u1D465 + u1D466 = 3 u1D465 + u1D466 = 2 We have three possibilities: 1. The lines intersect at one point. The system is consistent with exactly one solution. The equations are independent .
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