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The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:
- a)One solution
- b)Infinitely many solutions
- c)No solutions
- d)Two solutions
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 ha...
We have a1, a2 the coefficients of x2,b1 and b2 coefficients of x and c1 and c2 the constant terms.
So,
a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.
So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.Most Upvoted Answer
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 ha...
We have a1, a2 the coefficients of x2,b1 and b2 coefficients of x and c1 and c2 the constant terms.So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.
So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.Free Test
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Community Answer
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 ha...
Understanding the Given Equations
The equations provided are:
1. \(x + y + 10 = 0\)
2. \(x + y - 7 = 0\)
To analyze the relationship between these two equations, we can rewrite them in a more familiar form.
Rearranging the Equations
- Equation 1:
\(x + y = -10\)
- Equation 2:
\(x + y = 7\)
Identifying the Nature of Solutions
Both equations represent straight lines in a 2D plane:
- Line 1: All points \((x, y)\) that satisfy \(x + y = -10\).
- Line 2: All points \((x, y)\) that satisfy \(x + y = 7\).
Analyzing the Lines
- Both lines are parallel because they have the same slope (coefficient of \(x\) and \(y\) is 1 in both cases).
- Since they have different y-intercepts (\(-10\) and \(7\)), they will never intersect.
Conclusion
Since the two lines are parallel and do not intersect, they do not share any common points. Therefore, the system of equations has:
- No solutions.
Hence, the correct answer is option 'C'.
The equations provided are:
1. \(x + y + 10 = 0\)
2. \(x + y - 7 = 0\)
To analyze the relationship between these two equations, we can rewrite them in a more familiar form.
Rearranging the Equations
- Equation 1:
\(x + y = -10\)
- Equation 2:
\(x + y = 7\)
Identifying the Nature of Solutions
Both equations represent straight lines in a 2D plane:
- Line 1: All points \((x, y)\) that satisfy \(x + y = -10\).
- Line 2: All points \((x, y)\) that satisfy \(x + y = 7\).
Analyzing the Lines
- Both lines are parallel because they have the same slope (coefficient of \(x\) and \(y\) is 1 in both cases).
- Since they have different y-intercepts (\(-10\) and \(7\)), they will never intersect.
Conclusion
Since the two lines are parallel and do not intersect, they do not share any common points. Therefore, the system of equations has:
- No solutions.
Hence, the correct answer is option 'C'.
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The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer?.
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:a)One solutionb)Infinitely many solutionsc)No solutionsd)Two solutionsCorrect answer is option 'C'. Can you explain this answer?.
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