Advertisements
Advertisements
प्रश्न
Find the value of k for which the system of equations has a unique solution:
2x + 3y = 5,
kx - 6y = 8
उत्तर
The given system of equations are
2x + 3y – 5 = 0
kx - 6y - 8 = 0
This system is of the form:
`a_1x+b_1y+c_1 = 0 and a_2x+b_2y+c_2 = 0`
where, `a_1 = 2, b_1= 3, c_1= -5 and a_2 = k, b_2= -6, c_2= -8`
Now, for the given system of equations to have a unique solution, we must have:
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
`⇒ 2/k ≠ 3(−6)`
`⇒ k ≠ -4`
Hence, k ≠ -4
APPEARS IN
संबंधित प्रश्न
Draw the graph of
(i) x – 7y = – 42
(ii) x – 3y = 6
(iii) x – y + 1 = 0
(iv) 3x + 2y = 12
Solve for x and y:
2x – y + 3 = 0, 3x – 7y + 10 = 0
Solve for x and y:
`9/x - 4/y = 8, (13)/x + 7/y = 101`
Show that the following system of equations has a unique solution:
`x/3 + y/2 = 3, x – 2y = 2.`
Also, find the solution of the given system of equations.
For what value of k, the system of equations
x + 2y = 3,
5x + ky + 7 = 0
Have (i) a unique solution, (ii) no solution?
Also, show that there is no value of k for which the given system of equation has infinitely namely solutions
Find the value of k for which the system of linear equations has an infinite number of solutions:
2x + (k – 2)y = k,
6x + (2k - 1)y = (2k + 5).
Find the value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution.
Solve for x and y: `3/(x+y) + 2/(x−y) = 2, 9/(x+y) – 4/(x−y) = 1`
Solve for x:
Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.
