Advertisements
Advertisements
प्रश्न
Find the value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has infinite nonzero solutions.
उत्तर
The given system is
3x + 5y = 0 ……(i)
kx + 10y = 0 ……(ii)
This is a homogeneous system of linear differential equation, so it always has a zero solution i.e., x = y = 0.
But to have a non-zero solution, it must have infinitely many solutions.
For this, we have
`(a_1)/(a_2) = (b_1)/(b_2)`
`⇒ 3/k = 5/10 = 1/2`
⇒ k = 6
Hence, k = 6.
APPEARS IN
संबंधित प्रश्न
Find the value of k for which each of the following system of equations have infinitely many solutions:
2x − 3y = 7
(k + 2)x − (2k + 1)y − 3(2k − 1)
Find the value of k for which each of the following system of equations has infinitely many solutions :
x + (k + 1)y =4
(k + 1)x + 9y - (5k + 2)
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n
Solve for x and y:
2x – y + 3 = 0, 3x – 7y + 10 = 0
Solve for x and y:
`10/(x+y) + 2/(x−y) = 4, 15/(x+y) - 9/(x−y) = -2, where x ≠ y, x ≠ -y.`
Find the value of k for which the system of equations has a unique solution:
x – ky = 2,
3x + 2y + 5=0.
Show that the system of equations
6x + 5y = 11,
9x + 152 y = 21
has no solution.
The sum of a two-digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number,
Find a fraction which becomes `(1/2)` when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes `(1/3)` when 7 is subtracted from the numerator and 2 is subtracted from the denominator.
If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and `y/x` – 2.
