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If a pair of linear equations is consistent, then the lines are:
- a)Parallel
- b)Always coincident
- c)Always intersecting
- d)Intersecting or coincident
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If a pair of linear equations is consistent, then the lines are:a)Par...
Because the two lines definitely have a solution.
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Most Upvoted Answer
If a pair of linear equations is consistent, then the lines are:a)Par...
Explanation:
Consistent Linear Equations:
- When a pair of linear equations have a solution, they are said to be consistent.
- This means that the lines represented by the equations will intersect at a single point.
- The point of intersection is the solution to the system of equations.
Intersecting or Coincident Lines:
- If the lines represented by the pair of linear equations have different slopes, they will intersect at a single point.
- This is the most common scenario when dealing with consistent linear equations.
- However, if the equations represent the same line, then the lines are coincident.
- Coincident lines have infinite points of intersection, as they are essentially the same line.
Parallel Lines:
- In the case of parallel lines, the pair of linear equations have the same slope but different y-intercepts.
- When solving the system of equations, you will find that there is no point of intersection.
- This results in parallel lines that do not intersect at any point.
Therefore, if a pair of linear equations is consistent, the lines represented by the equations can either be intersecting or coincident. This means that the lines may intersect at a single point or coincide with each other, depending on the specific equations involved in the system.
Consistent Linear Equations:
- When a pair of linear equations have a solution, they are said to be consistent.
- This means that the lines represented by the equations will intersect at a single point.
- The point of intersection is the solution to the system of equations.
Intersecting or Coincident Lines:
- If the lines represented by the pair of linear equations have different slopes, they will intersect at a single point.
- This is the most common scenario when dealing with consistent linear equations.
- However, if the equations represent the same line, then the lines are coincident.
- Coincident lines have infinite points of intersection, as they are essentially the same line.
Parallel Lines:
- In the case of parallel lines, the pair of linear equations have the same slope but different y-intercepts.
- When solving the system of equations, you will find that there is no point of intersection.
- This results in parallel lines that do not intersect at any point.
Therefore, if a pair of linear equations is consistent, the lines represented by the equations can either be intersecting or coincident. This means that the lines may intersect at a single point or coincide with each other, depending on the specific equations involved in the system.
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If a pair of linear equations is consistent, then the lines are:a)Parallelb)Always coincidentc)Always intersectingd)Intersecting or coincidentCorrect answer is option 'D'. Can you explain this answer?
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