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On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14?
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On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whet...
Comparing the Ratios:
- Given equations: 3/2x + 5/3y = 7 and 9x - 10y = 14
- Let's compare the ratios of coefficients for x, y, and constants in the two equations:
- For x: 3/2 / 9 = 1/6
- For y: 5/3 / -10 = -1/2
- For constants: 7 / 14 = 1/2
Analysis:
- The ratios for x, y, and constants do not match, indicating that the system of equations is inconsistent.
- Inconsistent systems have no solution, meaning the two lines represented by the equations do not intersect at any point in the coordinate plane.
- This can also be visually verified by plotting the two equations on a graph. Since the lines do not intersect, they are parallel and inconsistent.
Explanation:
- When comparing the ratios of coefficients and constants in the two equations, we observe that they do not match.
- This mismatch indicates that the system of equations is inconsistent, meaning there is no solution that satisfies both equations simultaneously.
- Inconsistent systems typically have parallel lines that do not intersect, as is the case with these equations.
- Therefore, the pair of linear equations 3/2x + 5/3y = 7 and 9x - 10y = 14 is inconsistent.
By following the given guidelines and breaking down the answer into headings and bullet points, we have provided a detailed explanation of why the given pair of linear equations is inconsistent.
- Given equations: 3/2x + 5/3y = 7 and 9x - 10y = 14
- Let's compare the ratios of coefficients for x, y, and constants in the two equations:
- For x: 3/2 / 9 = 1/6
- For y: 5/3 / -10 = -1/2
- For constants: 7 / 14 = 1/2
Analysis:
- The ratios for x, y, and constants do not match, indicating that the system of equations is inconsistent.
- Inconsistent systems have no solution, meaning the two lines represented by the equations do not intersect at any point in the coordinate plane.
- This can also be visually verified by plotting the two equations on a graph. Since the lines do not intersect, they are parallel and inconsistent.
Explanation:
- When comparing the ratios of coefficients and constants in the two equations, we observe that they do not match.
- This mismatch indicates that the system of equations is inconsistent, meaning there is no solution that satisfies both equations simultaneously.
- Inconsistent systems typically have parallel lines that do not intersect, as is the case with these equations.
- Therefore, the pair of linear equations 3/2x + 5/3y = 7 and 9x - 10y = 14 is inconsistent.
By following the given guidelines and breaking down the answer into headings and bullet points, we have provided a detailed explanation of why the given pair of linear equations is inconsistent.
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On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14?
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On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14?.
On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On comparing the ratios aone by A2 b1 by b2 and C1 by C2 find out whether the following pairs of linear equation are consistent or inconsistent 3/2x+5/3y=7 ; 9x-10y=14?.
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