Question

Find the value of k for which the system of equation has a unique solution.

4x - 5y = k, 2x - 3y = 12​

Answer 1

Given :

• 4x - 5y = k.
• 2x - 3y = 12.

To Find :

The value of k

Solution :

We have, Condition.

• Linear Equations have under " Unique Solution "
• a1/a2 ≠ b1/b2.

A/Q,

• a1 = 4.
• a2 = 2.
• b1 = -5.
• b2 = -3.
• c1 = k.
• c2 = 12.

So,

$\tt \longmapsto\dfrac{a_1}{ a_2} \neq \dfrac{b_1}{ b_2 }$

$\tt \longmapsto\dfrac{4}{ 2} \neq \dfrac{ - 5}{ - 3 }$

$\tt \longmapsto\dfrac{4}{ 2} \neq \dfrac{ \cancel{ -} k}{ \cancel{ -} 12 }$

$\tt \longmapsto\dfrac{4}{ 2} \neq \dfrac{ k}{ 12 }$

$\tt \longmapsto\dfrac{4}{ \cancel2} \neq \dfrac{ k}{ \cancel{12} }$

$\tt \longmapsto k \neq24.$

Therefore, the value of k is 24.