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Which of the following pairs of equations represent inconsistent system?
- a)3x – y = -8 3x – y = 24
- b)5x – y = 10 10x – 2y = 20
- c)3x – 2y = 8 2x + 3y = 1
- d)lx – y = m x + my = l
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following pairs of equations represent inconsistent syste...
is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent.3x – y = -8 ,3x – y = 24
3x – y +8=0 ,3x – y -24=0
So,
Therefore the equations are inconsistent.Most Upvoted Answer
Which of the following pairs of equations represent inconsistent syste...
Inconsistent System of Equations
An inconsistent system of equations is a system that has no solutions. In other words, the lines representing the equations do not intersect and are parallel to each other.
Identifying an Inconsistent System of Equations
To identify an inconsistent system of equations, we need to check if the lines are parallel. This can be done by comparing the slopes of the lines. If the slopes are equal, the lines are parallel and the system is inconsistent.
Example
Let's check each pair of equations given in the question to identify which one represents an inconsistent system:
a) 3x + y = -8
3x + y = 24
The slopes of both equations are the same (3), which means they are parallel. Therefore, this system is inconsistent.
b) 5x + y = 10
10x + 2y = 20
The slopes of the equations are not equal. We can rewrite the second equation as 5x + y = 10, which is equivalent to the first equation. This means the lines are the same and the system is consistent.
c) 3x + 2y = 8
2x + 3y = 1
The slopes of the equations are not equal. Therefore, the lines intersect and the system is consistent.
d) lx + y = m
x + my = l
The slopes of the equations are not equal. Therefore, the lines intersect and the system is consistent.
Conclusion
The pair of equations that represents an inconsistent system is option 'a': 3x + y = -8 and 3x + y = 24.
An inconsistent system of equations is a system that has no solutions. In other words, the lines representing the equations do not intersect and are parallel to each other.
Identifying an Inconsistent System of Equations
To identify an inconsistent system of equations, we need to check if the lines are parallel. This can be done by comparing the slopes of the lines. If the slopes are equal, the lines are parallel and the system is inconsistent.
Example
Let's check each pair of equations given in the question to identify which one represents an inconsistent system:
a) 3x + y = -8
3x + y = 24
The slopes of both equations are the same (3), which means they are parallel. Therefore, this system is inconsistent.
b) 5x + y = 10
10x + 2y = 20
The slopes of the equations are not equal. We can rewrite the second equation as 5x + y = 10, which is equivalent to the first equation. This means the lines are the same and the system is consistent.
c) 3x + 2y = 8
2x + 3y = 1
The slopes of the equations are not equal. Therefore, the lines intersect and the system is consistent.
d) lx + y = m
x + my = l
The slopes of the equations are not equal. Therefore, the lines intersect and the system is consistent.
Conclusion
The pair of equations that represents an inconsistent system is option 'a': 3x + y = -8 and 3x + y = 24.
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Community Answer
Which of the following pairs of equations represent inconsistent syste...
A is right a1/a2=b1/b2not equals to c1/c2 so it is inconsistent...
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Which of the following pairs of equations represent inconsistent system?a)3x – y = -8 3x – y = 24b)5x – y = 10 10x – 2y = 20c)3x – 2y = 8 2x + 3y = 1d)lx – y = m x + my = lCorrect answer is option 'A'. Can you explain this answer?
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