Question

for what value of k the pair of equation 4x-3y=9,
2x +ky =11 has no solution​

Answer 1

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Given:-

• $\sf Equation_{1}$ = 4x-3y = 9
• $\sf Equation_{2}$ = 2x+ky = 11

To find:-

• value of K for which the above two equations have no Solution

Property to be used:-

• For no solution, the following property is used:-

:$\implies$ $\underline{\boxed{\sf \dfrac{a_{1}}{a_{2}} = \dfrac{b_{1}}{b_{2}} ≠ \dfrac{c_{1}}{c_{2}}}}$

here,

• $\sf a_{1}$ = 4
• $\sf a_{2}$ = 2
• $\sf b_{1}$ = -3
• $\sf b_{2}$ = K
• $\sf c_{1}$ = -9
• $\sf c_{2}$ = -11

Solution:-

:$\implies$ $\sf\dfrac{4}{2}$ = $\sf\dfrac{-3}{K}$

:$\implies$ $\sf 2 = \dfrac{-3}{K}$

:$\implies$ $\sf K = \dfrac{-3}{2}$

hence, the required answer states that:-

:$\implies$ K = -3/2.

Note:- when there is no Solution, it means that the lines are parallel to each other

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Additional information:-

To find the value for unique solution, following property is used:-

:$\implies$ $\underline{\boxed{\sf \dfrac{a_{1}}{a_{2}} ≠ \dfrac{b_{1}}{b_{2}}}}$

• this means that the lines are intersecting at one unique point

To find the value for infinite many Solutions, following property is used:-

:$\implies$ $\underline{\boxed{\sf \dfrac{a_{1}}{a_{2}} = \dfrac{b_{1}}{b_{2}} = \dfrac{c_{1}}{c_{2}}}}$

• this means that the lines are coinident to each other

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Answer 2

Answer:

$\frac{-3}{2}$ is the required value of k.

Step-by-step explanation:

Explanation:

Given in the question that, 4x - 3y = 9 and 2x + ky = 11.

As we know that, there won't be a solution if

$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

• An inconsistent pair of linear equations is the name given to this kind of equational system.

• If the lines are parallel on the graph, the system of equations cannot be solved.

Step 1:

We have,

4x - 3y -9 = 0 and 2x + ky - 11 = 0

Condition for no solution, $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.

So we have, $a_1 = 4 , b_1 = -3 and c_1 = -9$$,a_2 = 2 , b _2 = k and c_2 = -11$

⇒$\frac{4}{2} = \frac{-3}{k} \neq \frac{-9}{-11}$

⇒ 4k = -3× 2

⇒ 4k = -6

⇒ k = $\frac{-6}{4}$ = $\frac{-3}{2}$.

Final answer:

Hence, $\frac{-3}{2}$ is the required value of k.

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