 # 6.1 – Graphing Systems of Equations

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6.1 – Graphing Systems of Equations

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. 2y = -2x – 4 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 y = -x + 1 y = x – 3 y = -x – 2

Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. a. y = -x + 1 y = x – 3 One Sol. b. y = -x + 1 y = -x – 2 No Sol. c. y = -x – 2 Infinite Sol. y = -x + 1 y = x – 3 y = -x – 2

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1

Ex. 2 Graph each system of equations
Ex. 2 Graph each system of equations. Determine if the system has no, one, or infinitely many solutions. If it has one solutions, name it. a. y = 2x – 1 m = 2, b = -1 y = -2x – 1 m = -2, b = -1 One (0,-1)

b. 2x + 3y = 6 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12

b. 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 m = -2 , b = 2 3 -4x – 6y = -12 -6y = 4x – 12 Same line, therefore infinite sol.

c. 2x + y = 1 y = -2x – 1

c. 2x + y = 1 y = -2x + 1 m = -2, b = 1 y = -2x – 1 m = -2, b = -1 Parallel lines, therefore no sol.