Question

If the system of linear equation 2x+ 3y =5 and k x +9y =12 has a unique then find apportiate number of k

Answer 1

Hi,

Here is your answer

Given:

2x+3y=5

kx+9y=12

To Find:

The value of k

Solution:

Since the equations have unique solution,

$\frac{a1}{a2} \neq \frac{b1}{b2}$

Where a1=2,a2=k,b1=3,b2=9

Substitute these in the above equation.

We get,

$\frac{2}{k} \neq \frac{3}{9}$

Solving it we get,

$k\neq 6$

Therefore k can take any value except 6 for the pair of equations to have a unique solution.

Notes:

1. If a pair of equation has a unique solution,

$\frac{a1}{a2} \neq \frac{b1}{b2}$

2. If a pair of equations have infinite number of solutions,

$\frac{a1}{a2} =\frac{b1}{b2} =\frac{c1}{c2}$

3. If a pair of equations has no solution

$\frac{a1}{a2} =\frac{b1}{b2} \neq \frac{c1}{c2}$

Hope this helps you.