Advertisements
Advertisements
प्रश्न
Find the value of k for which the system of equations has a unique solution:
x – ky = 2,
3x + 2y + 5=0.
उत्तर
The given system of equations are
x - ky – 2 = 0
3x + 2y + 5 = 0
This system of equations is of the form:
`a_1x+b_1y+c_1 = 0 and a_2x+b_2y+c_2 = 0`
where,` a_1 = 1, b_1= -k, c_1= -2 and a_2 = 3, b_2 = 2, c_2 = 5`
Now, for the given system of equations to have a unique solution, we must have:
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
⇒ `1/3 ≠ −k/2`
⇒ `k ≠ - 2/3`
Hence, `k ≠ - 2/3`.
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the following system of equations has a unique solution:
4x + ky + 8 = 0
2x + 2y + 2 = 0
Find the value of k for which each of the following system of equations has infinitely many solutions :
2x +3y = k
(k - 1)x + (k + 2)y = 3k
Find the value of k for which each of the following system of equations have no solution
x + 2y = 0
2x + ky = 5
Find the values of a and b for which the following system of equations has infinitely many solutions:
3x + 4y = 12
(a + b)x + 2(a - b)y = 5a - 1
Find the values of a and b for which the following system of equations has infinitely many solutions:
2x + 3y = 7
(a - 1)x + (a + 1)y = (3a - 1)
Solve for x and y:
`(x + y - 8)/2 = (x + 2y -14)/3 = (3x + y - 12)/11`
Solve for x and y:
`x + y = a + b, a x – by = a^2 – b^2`
The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes `3/4`. Find the fraction.
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
2x + 3y = 7 and 2px + py = 28 – qy,
if the pair of equations have infinitely many solutions.
