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Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)
Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of the
homogeneous system of equations with unknowns x and y, then which of the following statement is true?
homogeneous system of equations with unknowns x and y, then which of the following statement is true?
- a)A is true and R is the correct explanation of A
- b)A is false and R is not a correrct explanation of A
- c)A is true and R is false
- d)A is false and R is true
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions o...
Homogeneous system of linear equations are of the form ax+by=0 and cx+dy=0. These lines pass through the origin. Thus, there is always at least one solution, the point (0,0).So, Homogeneous system of linear is always consistent, meaning that it has at least one solution which is (0,0). So B is the exact explanation.
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Most Upvoted Answer
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Explanation:
Statement A: Homogeneous system of linear equations is always consistent.
- A homogeneous system of linear equations is a system where all the constant terms on the right-hand side of the equations are zero.
- A homogeneous system of linear equations always has at least one solution, which is the trivial solution where all variables are equal to zero.
- Therefore, statement A is true because a homogeneous system of linear equations is always consistent.
Statement R: x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y.
- In a homogeneous system of linear equations, the trivial solution where all variables are equal to zero is always a solution.
- For example, in the system of equations x + y = 0 and 2x - y = 0, the solution x = 0, y = 0 satisfies both equations.
- Therefore, statement R is true because x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y.
Conclusion:
- Statement A is true and statement R is the correct explanation of statement A.
- Therefore, option 'A' is the correct answer.
Statement A: Homogeneous system of linear equations is always consistent.
- A homogeneous system of linear equations is a system where all the constant terms on the right-hand side of the equations are zero.
- A homogeneous system of linear equations always has at least one solution, which is the trivial solution where all variables are equal to zero.
- Therefore, statement A is true because a homogeneous system of linear equations is always consistent.
Statement R: x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y.
- In a homogeneous system of linear equations, the trivial solution where all variables are equal to zero is always a solution.
- For example, in the system of equations x + y = 0 and 2x - y = 0, the solution x = 0, y = 0 satisfies both equations.
- Therefore, statement R is true because x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y.
Conclusion:
- Statement A is true and statement R is the correct explanation of statement A.
- Therefore, option 'A' is the correct answer.
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Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?
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Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?.
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Pair of Linear Equation in two variables" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)Q. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of thehomogeneous system of equations with unknowns x and y, then which of the following statement is true?a)A is true and R is the correct explanation of Ab)A is false and R is not a correrct explanation of Ac)A is true and R is falsed)A is false and R is trueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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