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2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution?
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2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear...
Explanation of Pair of Linear Equations
Given Equations:
- 2x + 3y - 9 = 0
- 4x + 6y - 18 = 0
Checking for Consistency:
To determine if the pair of linear equations has a solution, we need to check if they are consistent, inconsistent, or dependent.
Consistency:
- Two equations are consistent if they have a unique solution.
- Inconsistent if they have no solution.
- Dependent if they have infinitely many solutions.
Comparing Coefficients:
- By comparing the coefficients of x and y in both equations, we can see that they are multiples of each other.
- This implies that the two equations represent the same line.
Dependent Equations:
- Since the two equations are dependent, they have infinitely many solutions.
- In this case, any point on the line represented by the equations will satisfy both equations simultaneously.
Conclusion:
- The given pair of linear equations are dependent and have infinitely many solutions.
- The equations represent the same line in the xy-plane.
- Therefore, the solution set is the set of all points on the line represented by the equations.
Given Equations:
- 2x + 3y - 9 = 0
- 4x + 6y - 18 = 0
Checking for Consistency:
To determine if the pair of linear equations has a solution, we need to check if they are consistent, inconsistent, or dependent.
Consistency:
- Two equations are consistent if they have a unique solution.
- Inconsistent if they have no solution.
- Dependent if they have infinitely many solutions.
Comparing Coefficients:
- By comparing the coefficients of x and y in both equations, we can see that they are multiples of each other.
- This implies that the two equations represent the same line.
Dependent Equations:
- Since the two equations are dependent, they have infinitely many solutions.
- In this case, any point on the line represented by the equations will satisfy both equations simultaneously.
Conclusion:
- The given pair of linear equations are dependent and have infinitely many solutions.
- The equations represent the same line in the xy-plane.
- Therefore, the solution set is the set of all points on the line represented by the equations.
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2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution?
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2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution?.
2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2x + 3 Y - 9 - 0 and Forex+ 6y minus 18 minus zero this pair of linear equation have – solution?.
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