System A System B System C 1 Line 1: y= X 1 Line 1: y= - x+2 Line 1: y=x+1 2 1 -x+3 1. Line 2: y= Line 2: x+2y=4 Line 2: y= 2* L2 LI 1.2 L2 4- This system of equations is: This system of equations is: This system of equations is: consistent independent consistent independent consistent dependent O inconsistent consistent independent consistent dependent consistent dependent inconsistent inconsistent This means the system has: This means the system has: This means the system has: O a unique solution O a unique solution O a unique solution Solution: 1D Solution: OD Solution: 0D O infinitely many solutions no solution O infinitely many solutions O no solution infinitely many solutions no solution

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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Question

Classifying systems of linear equations from graphs

System A
System B
System C
1
Line 1: y= X
1
Line 1: y= -
x+2
Line 1: y=x+1
2
1
-x+3
1.
Line 2: y=
Line 2: x+2y=4
Line 2: y=
2*
L2
LI
1.2
L2
4-
This system of equations is:
This system of equations is:
This system of equations is:
consistent independent
consistent independent
consistent dependent
O inconsistent
consistent independent
consistent dependent
consistent dependent
inconsistent
inconsistent
This means the system has:
This means the system has:
This means the system has:
O a unique solution
O a unique solution
O a unique solution
Solution: 1D
Solution: OD
Solution: 0D
O infinitely many solutions
no solution
O infinitely many solutions
O no solution
infinitely many solutions
no solution
Transcribed Image Text:System A System B System C 1 Line 1: y= X 1 Line 1: y= - x+2 Line 1: y=x+1 2 1 -x+3 1. Line 2: y= Line 2: x+2y=4 Line 2: y= 2* L2 LI 1.2 L2 4- This system of equations is: This system of equations is: This system of equations is: consistent independent consistent independent consistent dependent O inconsistent consistent independent consistent dependent consistent dependent inconsistent inconsistent This means the system has: This means the system has: This means the system has: O a unique solution O a unique solution O a unique solution Solution: 1D Solution: OD Solution: 0D O infinitely many solutions no solution O infinitely many solutions O no solution infinitely many solutions no solution
Expert Solution
Step 1

When two lines are parallel then their equations are not solvable that is inconsistent and will have no solution.

When two lines are overlapping then their equations are solvable that is consistent but have dependent solutionand will have infinite many solution.

When two lines are intersecting then their equations are solvable that is consistent and will have unique solution.

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