Math 20-1 Chapter 8 Systems of Equations

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Math 20-1 Chapter 8 Systems of Equations Teacher Notes 8.2 Solving Systems Algebraically

8.2 Solve a Linear-Quadratic System of Equations Algebraically Solve the following system of equations. Substitution Method Substitute x – 15 for y in the quadratic equation and simplify Substitute to determine the corresponding values of y. For x = –5 For x = 4 The two solutions are (–5, –20) and (4, –11). 8.2.1

Solve a Linear-Quadratic System of Equations Algebraically Verify the solutions (–5, –20) and (4, –11). For (–5, –20) For (4, –11) Both solutions are correct. The two solutions are (–5, –20) and (4, –11). 8.2.2

Solve a Linear-Quadratic System of Equations Algebraically Solve the following system of equations. Elimination Method Align the terms in the same degree. Subtract to eliminate the y-term Since the quadratic term is in the variable x, eliminate the y-term. – ( ) Solve the resulting equation. Determine the corresponding values of y. The two solutions are (–3, 0) and (1, 4). 8.2.3

Solve a Linear-Quadratic System of Equations Algebraically Verify the solutions (–3, 0) and (1, 4). For (–3, 0) For (1, 4) Both solutions are correct. The two solutions are (–3, 0) and (1, 4). 8.2.4

Your Turn Solve the system: The two solutions are (0, –4) and (5, 6). 8.2.5

Solve a Linear-Quadratic System of Equations Algebraically A main support cable of a suspension bridge hangs in the shape of a parabola modeled by the equation y = .25x2 -10x + 100, where x represents the number of feet from its left-most support and where y represents the number of feet the cable is above the road deck for any given x value. A surveyor’s line of sight is shown in the diagram below. (a) Write an equation for the line of sight in y = mx + b form. (Hint – The line of sight goes through the origin and (40,100) .) (b) Find the coordinates of the point where the line of sight first intersects the cable, point P, by solving the system of equations consisting of y = .25x2 -10x + 100 and your linear equation from part (a). Line of Sight 8.2.6

Solve a Linear-Quadratic System of Equations Algebraically a) Slope of the line of sight is y-intercept is 0 The equation of the line of sight is y = 2.5x b) Solve the system The line of sight intersects the cable at the point (10, 25). 8.2.7

Solve a Quadratic-Quadratic System of Equations Algebraically Solve the following system of equations. The two solutions are (5,43) and (2, 7). 8.2.8

Solve a Quadratic-Quadratic System of Equations Algebraically Verify the solutions (5, 43) and (2, 7). For (5, 43) For (2, 7) Both solutions are correct. The two solutions are (5, 43) and (2, 7). 8.2.9

Solve a Quadratic-Quadratic System of Equations Algebraically Your Turn Solve the system: The two solutions are (1, 6) and . 8.2.10

Problem Solving: Solve the following system of equations.

Problem Solving: Solve the system.

Problem Solving: Determine the values of m and n if (3, 4) is a solution to the following system of equations.

Assignment Suggested Questions: Page 451: 2, 3a,d, 4a,c,e, 5c, 6, 8, 10, 13, 16