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The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are
1. consistent with unique
2. inconsistent
3. consistent with infinite solutions?
1. consistent with unique
2. inconsistent
3. consistent with infinite solutions?
Most Upvoted Answer
The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with un...
Consistency of the System of Equations:
To determine the consistency of the system of equations, we need to analyze the slopes of the lines formed by the given equations. This can be done by comparing the coefficients of x and y in each equation.
Equation 1: 2x + 3y + 4 = 0
- Slope of the line: -2/3
- Since all three equations have different slopes, they are not parallel.
Equation 2: 3x + 4y + 6 = 0
- Slope of the line: -3/4
Equation 3: 4x + 5y + 8 = 0
- Slope of the line: -4/5
Determining Consistency:
- If the slopes of the lines are different, the system of equations is consistent.
- If the slopes are the same, the system is either consistent with infinite solutions or inconsistent.
Analysis:
- Since the slopes of the lines formed by the given equations are all different, the system of equations is consistent.
- Also, the equations do not form parallel lines, which means they intersect at a single point.
- Therefore, the system is consistent with a unique solution.
Conclusion:
The given system of equations 2x + 3y + 4 = 0, 3x + 4y + 6 = 0, and 4x + 5y + 8 = 0 is consistent with a unique solution.
To determine the consistency of the system of equations, we need to analyze the slopes of the lines formed by the given equations. This can be done by comparing the coefficients of x and y in each equation.
Equation 1: 2x + 3y + 4 = 0
- Slope of the line: -2/3
- Since all three equations have different slopes, they are not parallel.
Equation 2: 3x + 4y + 6 = 0
- Slope of the line: -3/4
Equation 3: 4x + 5y + 8 = 0
- Slope of the line: -4/5
Determining Consistency:
- If the slopes of the lines are different, the system of equations is consistent.
- If the slopes are the same, the system is either consistent with infinite solutions or inconsistent.
Analysis:
- Since the slopes of the lines formed by the given equations are all different, the system of equations is consistent.
- Also, the equations do not form parallel lines, which means they intersect at a single point.
- Therefore, the system is consistent with a unique solution.
Conclusion:
The given system of equations 2x + 3y + 4 = 0, 3x + 4y + 6 = 0, and 4x + 5y + 8 = 0 is consistent with a unique solution.
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The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions?
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The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions?.
The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 2x+3y+4=0;3x+4y+6=0and 4x+5y+8=0 are1. consistent with unique 2. inconsistent 3. consistent with infinite solutions?.
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