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1 Unit 9 Section 6.1-6.3 Notes Section 6.1 Vocabulary 90. System of Linear Equations: a set of two or more _________________ _________________ containing two or more variables. 91. Solution of a System of Linear Equations: is an ____________ ____________ that satisfies each equation in the system. This is the intersection point of two lines. NOTE: Systems of linear equations are used to represent situations and solve problems involving consumer economics, finance, and geometry. Section 6.1 Notes (Solving Systems by Graphing) EQ: I. Identifying Solutions of Systems (Recall a solution is an ordered pair that makes both equations true.) Example: Tell whether the ordered pair is a solution of the given system. a. (4, 1); x + 2y = 6 x–y=3 Check the ordered pair in both equations 4 + 2(1) = 6 6=6 4–1=3 3=3 Since the ordered pair made both equations true it is a solution for the system. The ordered pair is the intersection of the two lines. Try: (-1, 2); 2x + 5y = 8 3x – 2y = 5 2 II. Solving a System of Linear Equations by Graphing (Recall that to graph a line you plot the y-intercept and use the slope to find additional points on the line) Example: Solve each system by graphing. Check your answer. a. y = x – 3 y = -x – 1 b. x + y = 0 y = -1/2x + 1 c. y = -2x – 1 y=x+5 3 d. y = 1/3x – 3 2x + y = 4 4 Section 6.2 Notes (Solving Systems by Substitution #92) EQ: How do you solve a linear system using substitution? Note: In the substitution method we are going to substitute one equation into the other. Example: Solve each system by substitution a. y = 2x y=x+5 b. 2x + y = 5 y=x–4 c. x + 4y = 6 x+y=3 5 d. 4y – 5x = 9 x – 4y = 11 Try: 2x + y = -4 x + y = -7 -2x + y = 8 3x + 2y = 9 6 Section 6.3 Notes (Solving Systems by Elimination #93) Note: In the elimination method we will be “eliminating” one of the terms in the equations. EQ: How do you solve a linear system using elimination? Example: Solve each system using elimination. a. x – 2y = -19 5x + 2y = 1 b. 3x + 4y = 18 -2x + 4y = 8 c. 2x + y = 3 -x + 3y = -12 7 d. 7x – 12y = -22 5x – 8y = -14 Try: 3x + 3y = 15 -2x + 3y = -5 2x + 5y = 26 -3x – 4y = -25