# Find the Value of K for Which the System Kx + 2y = 5 3x + Y = 1 Has (I) a Unique Solution, and (Ii) No Solution. - Mathematics

Find the value of k for which the system
kx + 2y = 5
3x + y = 1
has (i) a unique solution, and (ii) no solution.

#### Solution

The given system of equation may be written as

kx + 2y - 5 = 0

3x + y - 1 = 0

It is of the form

a_1x + b_1y + c_1 = 0

a_2x + b_2y + c_2 = 0

Where a_1 = k, b_1 = 2, c_1 = -5

And a_2 = 3, b_2 = 1, c_2 = -1

Where, a_1 = k, b_1 = 2, c_1 = -5

And a_2 = 3, b_2 = 1, c_2 = -1

1) The given system will have a unique solution, if

a_1/a_2 != b_1/b_2

=> k/3 != 2/1

=> k != 6

So, the given system of equations will have a unique solution, if k != 6

2) The given system will have no solution, if

a_1/a_2 - b_1/b_2 != c_1/c_2

we have

b_1/b_2 = 2/1 and c_1/c_2 = (-5)/(-1) = 5/1

Clearly b_1/b_2 != c_1/c_2

So, the given system of equations will have no solution, if

a_1/a_2 = b_1/b_2

=> k/3 = 2/1

=> k = 6

Hence, the given system of equations will have no solution if k = 6

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 5 | Page 73