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Warm-Up 8/13/2010 Solve each equation for the indicated variable 1.) 2 x y 5; y y 2x 5 2.) x 2 y 3; x x 2y 3 3.) 3 x 4 y 12; y 3 y x3 4 4 x y4 3 4.) 3 x 4 y 12; x Any questions over HW? 1.3 Solve Systems of Equations Algebraically page 13 System of Equations Two or more equations with the same variables. x + y = 11 3x – y = 5 (4, 7) is the unique solution (4, 7) is a solution to BOTH equations Ex. 1: Solve by substitution 2x y 6 3x 4 y 4 So…(4 , -2) is the solution to the system Solving a System of Equations Graphing 1) Put each equation in slope-intercept form 2) Graph *plot the y-intercept *use the slope to find another point 3) Determine the solution Substitution 1) Solve one of the equations for one of the variables. 2) Substitute into the other equation 3) Solve 4) Substitute to solve for the remaining variable. Solve the system by substitution 3x 4 y 4 x 2y 2 (-8, 5) Ex. 3 Solve by elimination (linear combination) 3x 4 y 1 3x 2 y 0 1 1 , 3 2 Solving a System of Equations Graphing 1) Put each equation in slope-intercept form 2) Graph *plot the y-intercept *use the slope to find another point 3) Determine the solution Substitution Elimination 1) Solve one of the equations for one of the variables. 1) Choose a variable to eliminate 2) Substitute into the other equation 2) Make coefficients opposite numbers by multiplying 3) Solve 3) Add the equations 4) Substitute to solve for the remaining variable. 4) Substitute to solve for the remaining variable. Goal: Find Unique Solutions (ordered pairs) Ex. 3 solve by elimination 3x 3 y 15 2 x 6 y 22 (2, 3) Ex. 4 Use elimination to solve 5x + 4y = 11 3x – 5y = -23 Practice Problems 1.) 2y + x = 1 Use substitution 3y – 2x = 12 2.) 5x + 3y = 17 Use elimination -5x + 2y = 3 3.) 3x + 5y = 30 5x + 3y = 34 Use any method Homework Page 161 #2-12 even Page 166 #2-18 even