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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. - PowerPoint PPT Presentation
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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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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
2 2 2
y = -x + 1
y = x – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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
2 2 2 y = -x – 2
y = -x + 1
y = x – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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 – 2
y = -x + 1
y = x – 3y = -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 – 2
Infinite Sol.
y = -x + 1
y = x – 3y = -x – 2
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 sol. @ (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
y = -⅔x + 2
b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
y = -⅔x + 2
b. 2x + 3y = 6
3y = -2x + 6
y = -⅔x + 2
m = -2 , b = 2
3
-4x – 6y = -12
-6y = 4x – 12
y = -⅔x + 2
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.
