A12 - Systems of Equations VJ joma - Systems of Equations Mathematics 17 Institute of Mathematics University of the Philippines-Diliman Lecture 12 Math

A12 - Systems of Equations VJ joma - Systems of Equations...

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Systems of Equations Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 12 Math 17 (UP-IMath) Systems Lec 12 1 / 29
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Outline 1 Two Linear Equations in Two Variables 2 Examples of Systems Involving Quadratic Equations A Line and a Parabola A Line and a Circle 3 Three Linear Equations in Three variables Math 17 (UP-IMath) Systems Lec 12 2 / 29
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Aim for this Lecture Previously: graphing lines, parabolas, circles Math 17 (UP-IMath) Systems Lec 12 3 / 29
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Aim for this Lecture Previously: graphing lines, parabolas, circles Learn techniques in solving systems of equations Math 17 (UP-IMath) Systems Lec 12 3 / 29
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Aim for this Lecture Previously: graphing lines, parabolas, circles Learn techniques in solving systems of equations Solve algebraically for the intersections of graphs of equations Math 17 (UP-IMath) Systems Lec 12 3 / 29
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Aim for this Lecture Previously: graphing lines, parabolas, circles Learn techniques in solving systems of equations Solve algebraically for the intersections of graphs of equations Graph equations with their intersections Math 17 (UP-IMath) Systems Lec 12 3 / 29
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System of Equations Definition A system of equations is a set of two or more equations in several equations. A solution of a system is a solution common to all equations in the system. The solution set of a system is the set of all its solutions. Math 17 (UP-IMath) Systems Lec 12 4 / 29
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Two Linear Equations in Two Variables Definition A system of two linear equations in two variables has the form a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 where a 1 , a 2 , b 1 , b 2 , c 1 , c 2 2 . Math 17 (UP-IMath) Systems Lec 12 5 / 29
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Graphical Interpretation of Linear Systems Recall: A solution to an equation in two variables is a point on the graph of the equation. Math 17 (UP-IMath) Systems Lec 12 6 / 29
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Graphical Interpretation of Linear Systems Recall: A solution to an equation in two variables is a point on the graph of the equation. For systems of two linear equations in two variables, each equation represents a line. Math 17 (UP-IMath) Systems Lec 12 6 / 29
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Graphical Interpretation of Linear Systems Recall: A solution to an equation in two variables is a point on the graph of the equation. For systems of two linear equations in two variables, each equation represents a line. Example. Solve the system 3 x - 4 y = 1 2 x + 3 y = 12 Math 17 (UP-IMath) Systems Lec 12 6 / 29
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Graphical Interpretation of Linear Systems Recall: A solution to an equation in two variables is a point on the graph of the equation. For systems of two linear equations in two variables, each equation represents a line. ) A solution to the system is a point on both lines. Example. Solve the system 3 x - 4 y = 1 2 x + 3 y = 12 Math 17 (UP-IMath) Systems Lec 12 6 / 29
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Graphical Interpretation of Linear Systems Recall: A solution to an equation in two variables is a point on the graph of the equation.
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