Question

find k if the solution is unique
x-ky=2 and 3x+2y=-5
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Answer 1

Answer:

,

The system of equation are

x - ky = 2

3x + 2y = - 5

To find, the value of k = ?

Here, a_{1} =1,b_{1} =-k,c_{1} =2 and

a_{2} =3,b_{2} =2,c_{2} =-5

The condition of the the system of equation has a unique solution

\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}

∴ \dfrac{1}{3} \neq \dfrac{-k}{2}

⇒ k\neq \dfrac{-2}{3}

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

The given equations are:

x-ky=2 and 3x+2y=-5

Since, these equations has unique solution, therefore

\frac{a_{1}}{a_{2}}{\neq}\frac{b_{1}}{b_{2}}

Here, a_{1}=1, a_{2}=3, b_{1}=-k and b_{2}=2

\frac{1}{3}{\neq}\frac{-k}{2}

Thus, if the system of linear equations has unique solution then \frac{1}{3}{\neq}\frac{-k}{2}.

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