Relationship of Coefficients with Number of Solutions
Relationship of Coefficients with Number of Solutions
RELATIONSHIP OF COEFFICIENTS WITH NUMBER OF SOLUTIONS:
System of a pair of linear equations in two variables :
The given system of a pair of linear equations in tw variables has either one solution, infinite solutions or no solution.
then the system has one (or unique) solution, and the system intersect each other at only one point.
then the given system has infinte solution and the system is called dependent. In this case, a pair od lines represented by the system coincides with each other. So the intersect each other at infinite number of points.
then the given system has no solution and hence the system is called inconsistent. 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.
Example : Check whether the pair of equation
and
SOLUTION
Hence the given system of a pair of equations in two variable is consistent.
By comparing the linear equation 2y + x + 4 = 0 with ax + by + c = 0, find the value of - b | |||
| Right Option : B | |||
| View Explanation | |||
By comparing the linear equation - 3y + 2x - 9 = 25 with ax + by + c = 0, find the value of -c. | |||
| Right Option : C | |||
| View Explanation | |||
The pair of equations : | |||
| Right Option : D | |||
| View Explanation | |||
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