The pair of equations  kx-4y=3 and 6x-12y=9 have a unique solution when value for k is all real numbers except ____.

# The pair of equations  have a unique solution when value for k is all real numbers except ____.

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### Solution:

The pair of equations  have a unique solution when value for k is all real numbers except 2.
Given systems of equations are .
A system of linear equations will have unique solution when $\frac{{a}_{1}}{{a}_{2}}\ne \frac{{b}_{1}}{{b}_{2}}$.
Here, ${a}_{1}=k,{b}_{1}=-4{,a}_{2}=6,{b}_{2}=-12.$
$⇒\frac{{a}_{1}}{{a}_{2}}=\frac{k}{6},\frac{{b}_{1}}{{b}_{2}}=\frac{-4}{-12}$
For the equations to have unique solutions, we should have,
$\frac{k}{6}\ne \frac{-4}{-12}$

Therefore, the value of k is all real numbers except 2.

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