Question

25. One of the equations of a pair of linear equations having unique solution, is 2x - y I =1. The other possible equation is : (a) 2x - y - 3 = 0 (b) 4x - 2y = 2 (C) 4x - 2y = 1 (d) 3x-y-5=0​

Answer 1

Given: One of the equations of a pair of linear equations having unique solution is 2x - y =1.

To find: The other equation

Explanation: The necessary condition for two equations ax+by+c=0 and px+qy+r= 0 to have a unique solution is:

a/p should not be equal to b/q.

Here, a= 2 and b= -1

Checking option (a) 2x-y-3=0:

Here, p= 2 and q= -1

a/p = 2/2

= 1

b/q = -1 / -1

= 1

Since they are equal they do not have a unique solution.

Checking option (b) 4x-2y=2:

Here, p= 4 and q= -2

a/p = 2/4

= 1/2

b/q = -1 / -2

= 1/2

Since they are equal they do not have a unique solution.

Checking option (c) 4x-2y=1:

Here, p= 4 and q= -2

a/p = 2/4

= 1/2

b/q = -1 / -2

= 1/2

Since they are equal they do not have a unique solution.

Checking option (d) 3x-y-5=0:

Here, p= 3 and q= -1

a/p = 2/3

b/q = -1 / -1

= 1

Since they are not equal they have a unique solution.

Therefore, a possible equation is option (d) 3x-y-5=0.