Advertisements
Advertisements
Question
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Advertisements
Solution
The given equations are
kx + 2y = 3
3x + 6y = 10
For a unique solution,
`a_1/a_2 ≠ b_1/b_2`
Where a1= k, a2 = 3, b1 = 2, b2 = 6.
`k/3 ≠ 2/6`
⇒ k ≠ 1
For all values of k except 1, the given linear equations will have a unique solution.
APPEARS IN
RELATED QUESTIONS
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
