Finite Chapter 2.1

Finite Chapter 2.1 - to find the other variable: 3x + 3 = 3...

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Math 120 SP08 SBrodnick 1 1 Chapter 2 : Systems of Linear Equations and Matrices 2.1 : Systems of Two Linear Equations in Two Unknowns 2 2.1: Systems of Two Linear Equations in Two Unknowns Example : 1. 4x - 2y = -6 is a linear equation in two unknowns, x and y Graph it y = 2x + 3 What’s one solution to the equation? 3 2.1: Systems of Two Linear Equations in Two Unknowns 2.Two linear equations in two unknowns: 3x + y = 3 and -3x + y = 3… how to find a solution? * Solving a system graphically : Graph both equations together 2 nd TRACE 5:Intersect Move cursor to intersection point ENTER 3 times 4 2.1: Systems of Two Linear Equations in Two Unknowns * Solving a system algebraically : Set equal and solve for x Use the method of elimination : 3x + y = 3 -3x + y = 3 1. add : 0x + 2y = 6 2. solve for one variable: 2y = 6, so y = 3 3. plug into either equation
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Unformatted text preview: to find the other variable: 3x + 3 = 3 3x = 0, so x = 0 Solution is (x, y) = (0, 3) OR 5 2.1: Systems of Two Linear Equations in Two Unknowns * Elimination : term and its opposite stacked on top of each other before you add Examples : Solve each system using elimination 3. 2x + 3y = 5 and 3x + 2y = 5 4. -0.3x + 0.5y = 0.1 and 0.1x 0.1y = 0.4 5. -2x + 3y = 15 and -10x + 15y = 12 6 2.1: Systems of Two Linear Equations in Two Unknowns * No Solution-- System is Inconsistent (if a solution exists, system is consistent ) 6. 5x + 2y = 1 and -10x 4y = -2 * Infinite Solutions-- System is Redundant (one variable is arbitrary ) 7. x y = 2 and 3x 6y = 12 * All possibilities accounted for: 1 Solution No Solution Infinite Solutions...
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