10_1 - Section 10.1 System of LINEAR equations Two...

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Section 10.1: System of LINEAR equations: Two Equations containing Two Variables Instructor: Ms. Hoa Nguyen ([email protected]) 1 Geometric View of Two Linear Equations containing Two Variables Reminder of Linear Equation : A linear equation containing two variables x, y is an equation of the form Ax + By = C , where A, B , and C are constants. The graph of a linear equation containing the variables x, y is a LINE in xy -space. Thus, a system of two linear equations containing the variables x, y is a PAIR of LINEs in xy -space. A system of two linear equations containing two variables : The above Figure shows 3 possible solutions of a system of two linear equations containing two variables: Exactly ONE solution (UNIQUE solution): the solution is given by the point of inter- section. NO solution. INFINITELY MANY solutions. Note : It is NOT possible for a linear system to have exactly two solutions. A system of equations is said to be consistent if the system has AT LEAST ONE solution.
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