Advertisements
Advertisements
प्रश्न
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n
उत्तर
The given system of equations may be written as
ax + by − c = 0
lx + my − n = 0
It is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = a, b_1 = b, c_1 = -c`
And `a_2 = l, b_2 = m,c_2 = -n`
For unique solution, we must have
`a_1/a_2 != b_1/b_2`
`=> a/l != b/m`
`=> am != bl`
Hence, `am != bl` is the required condition.
APPEARS IN
संबंधित प्रश्न
In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
2x + y - 5 = 0
4x + 2y - 10 = 0
Solve for x and y:
`1/(3x+y) + 1/(3x−y) = 3/4, 1/(2(3x+y)) - 1/(2(3x−y)) = −1/8`
Solve for x and y:
`1/(2(x+2y)) + 5/(3(3x−2y)) = - 3/2, 1/(4(x+2y)) - 3/(5(3x−2y)) = 61/60` where x + 2y ≠ 0 and 3x – 2y ≠ 0.
Solve for x and y:
`3/x + 6/y = 7, 9/x + 3/y = 11`
Solve for x and y:
`a^2x + b^2y = c^2, b^2x + a^2y = d^2`
Solve for x and y:
`x/a + y/b = a + b, x/(a^2)+ y/(b^2) = 2`
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
(2a – 1) x + 3y = 5, 3x + (b – 1)y = 2.
A man purchased 47 stamps of 20p and 25p for ₹10. Find the number of each type of stamps
Find the value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution.
Show that the system 2x + 3y -1= 0 and 4x + 6y - 4 = 0 has no solution.
