Q11 of 244 Page 124

Show that the system of equations

6x + 5y = 11, 9x + y = 21

Given: 6x + 5y = 11 – eq 1


9x + y = 21 ⇒ 18x + 15y = 42 – eq 2


Here,


a1 = 6, b1 = 5, c1 = - 11


a2 = 18, b2 = 15, c2 = - 42


Here,



= =


= =


Here,


= ≠


That is give system of equations are parallel lines, that is they don’t have any solutions.


∴ The system of equations has no solution.


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9

Find the value of k for which each of the following systems of equations has a unique solution:

kx + 3y = (k – 3), 12x + ky = k.

 10

Show that the system of equations

2x – 3y = 5, 6x – 9y = 15

 12

For what value of k does the system of equations

kx + 2y = 5, 3x – 4y = 10


have (i) a unique solution, (ii) no solution?

 13

For what value of k does the system of equations

x + 2y = 5, 3x + ky + 15 = 0


have (i) a unique solution, (ii) no solution?