Question

for what value of k , will the system of equation ......... x+ 2y= 5, 3x +ky -15= 0 has a unique solution ......plzzzzz

Answer 1

✒ HEY THERE!!!✒

$\huge{\bold{SOLUTION :- }}$

✒ Method Of Solution:

Given:

✒ Equation (1) : x+2y = 5

✒ Equation (2) : 3x+ky= 15

Now, ✒ Using Formula!

✒ For unique solution must be a1/a2≠ b1/b2

Now, Substitute the Given value in Equation!

Here, (a1 = 1 , b1 = 2) and (a2= 3, b2 = k)

✒ a1/a2≠ b1/b2

✒ 1/3≠ 2/k

✒ k ≠ 3×2

✒ k ≠6

Here, Value of k remain = ≠6

Note: For all value of k other than 6 ,the Given system of Equation will have a unique!

Hence, Value of k is 6.

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Answer 2

Answer:

For a system to have an unique solution a criteria must be followed.

Criteria:

$\bf{\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}}$

Here, a₁ is the coefficient of x in Equation 1 and a₂ is that of x in Equation 2. Similarly, b₁ and b₂ are coefficients of y in Equations 1 and 2.

a₁ = 1, a₂ = 3, b₁ = 2, b₂ = k

So, According to the criteria,

⇒ 1 / 3 ≠ 2 / k

⇒ k ≠ 2 × 3

⇒ k ≠ 6

Hence the value of k must not be equal to 6, but it can take other values.