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A system of two linear equations in two variables is inconsistent, if their graphs
- a)do not intersect at any point
- b)cut the x – axis
- c)intersect only at a point
- d)coincide
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A system of two linear equations in two variables is inconsistent, if ...
A system of two linear equations in two variables is inconsistent, if their graphsdo not intersect at any point. In this case, a pair of lines represented by the system are parallel to each other. so they do not intersect each other at any point.
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A system of two linear equations in two variables is inconsistent, if ...
Explanation:
Definition of Inconsistent System:
An inconsistent system of linear equations is a system where the equations do not have a common solution. In other words, the graphs of the two equations do not intersect at any point.
Graphical Representation:
- When two linear equations are inconsistent, their graphs do not intersect at any point on the coordinate plane.
- This means that the lines represented by the equations are parallel and will never meet.
Explanation of Options:
- Option 'a' is correct because an inconsistent system does not have any intersection point.
- Option 'b' is incorrect because if the graphs cut the x-axis, it means they have a common solution.
- Option 'c' is incorrect because if the graphs intersect at only one point, it means they have a unique solution.
- Option 'd' is incorrect because if the graphs coincide, it means they have infinitely many solutions.
Therefore, the correct answer is option 'a', as an inconsistent system of linear equations does not intersect at any point.
Definition of Inconsistent System:
An inconsistent system of linear equations is a system where the equations do not have a common solution. In other words, the graphs of the two equations do not intersect at any point.
Graphical Representation:
- When two linear equations are inconsistent, their graphs do not intersect at any point on the coordinate plane.
- This means that the lines represented by the equations are parallel and will never meet.
Explanation of Options:
- Option 'a' is correct because an inconsistent system does not have any intersection point.
- Option 'b' is incorrect because if the graphs cut the x-axis, it means they have a common solution.
- Option 'c' is incorrect because if the graphs intersect at only one point, it means they have a unique solution.
- Option 'd' is incorrect because if the graphs coincide, it means they have infinitely many solutions.
Therefore, the correct answer is option 'a', as an inconsistent system of linear equations does not intersect at any point.
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A system of two linear equations in two variables is inconsistent, if their graphsa)do not intersect at any pointb)cut the x – axisc)intersect only at a pointd)coincideCorrect answer is option 'A'. Can you explain this answer?
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