Advertisements
Advertisements
प्रश्न
Find the value of k for which each of the following systems of equations has infinitely many solutions :
4x + 5y = 3
kx + 15y = 9
उत्तर
The given system of equation is
4x + 5y -3 = 0
ks + 15y - 9 = 0
The system of equation is of the for
`a_1x + b_1y + c_1= 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = 4, b_1 = 5, c_1 = -3`
And `a_2 = k, b_2 = 15, c_2 = -9`
For a unique solution, we must have
`a_1/a_2 = b_1/b_2 = c_2/c_2`
`=> 4/k = 5/15 = (-3)/(-9)`
Now
`4/k = 5/15`
`=> 4/k = 1/3`
`=> k = 12`
Hence, the given system of equations will have infinitely many solutions, if k = 12
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
Find the value of k for which each of the following system of equations has infinitely many solutions :
\[kx + 3y = 2k + 1\]
\[2\left( k + 1 \right)x + 9y = 7k + 1\]
Find the values of k for which the system
2x + ky = 1
3x – 5y = 7
will have (i) a unique solution, and (ii) no solution. Is there a value of k for which the
system has infinitely many solutions?
Find the value of k for which the system of equations
8x + 5y = 9, kx + 10y = 15
has a non-zero solution.
A two-digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange their places. Find the number.
Places A and B are 160 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
A number consists of two digits whose sum is 10. If 18 is subtracted form the number, its digits are reversed. Find the number.
Find the value of k for which the system of equations 2x + 3y -5 = 0 and 4x + ky – 10 = 0 has infinite number of solutions.
Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.
The condition for the system of linear equations ax + by = c; lx + my = n to have a unique solution is ______.
