for what value of k the pair of equation 4x-3y = 9, 2x + k y = 11 has no solution
Answers
Given:
Two straight lines 4x – 3y = 9 and 2x + k = 11.
To Find:
The value of k for which the two lines do not have any solution.
Solution:
The given question can be solved by using the concepts of straight lines.
1. Consider two straight lines in the 2D coordinate system as ax + by + c = 0 and dx + ey + f = 0.
According to the concepts of straight lines, two lines do not intersect if they are parallel to each other.
2. Using the above property, two lines are said to be parallel if the coefficient of x in line 1 is the same as the coefficient of x in line 2 and the coefficient of y in line 1 must be the same as the coefficient of line 2.
3. Two parallel lines differ only by the constant value.
4. The given lines are 4x – 3y = 9 (Consider as equation 1) and 2x + k = 11(Consider as equation 2).
=> Multiply equation 2 with 2 on both the sides,
=> 4x + 2k = 22. Now, the modified equation 2 is has similar x coefficient with equation 1. For the two lines to have no solutions the y coefficient must be equal. Hence,
=> 2k = -3,
=> k = (-3/2).
Therefore, the value of k for which the given lines have no solutions is (-3/2).