Question 1- find the value of k for which the equation has unique solution . 1: 2x -3y= 1 Kx +5y=7?

Question

Answer

Answer

A 1/ a2 = b 1/b2 = c1 / c2
2/k is not equal to - 3/5 = 1/7
2/k is not equal to --3/5
-3k is not =10
k is not = 10 /-3

Answer

Solution:

Step 1: Write the given system of equations in matrix form

Let's write the system of equations in matrix form as follows:

AX = B

Where,

A = [2 -3] K 5

X = [x y]

B = [1 7]

Step 2: Find the determinant of matrix A

The system of equations has a unique solution if and only if the determinant of matrix A is not equal to zero.

Let's find the determinant of matrix A:

det(A) = (2*5*K) - (-3*K) = 10K + 3K = 13K

Step 3: Set the determinant of matrix A not equal to zero

To have a unique solution, the determinant of matrix A must not be equal to zero. Therefore, we set the determinant of matrix A not equal to zero as follows:

13K ≠ 0

K ≠ 0

Step 4: Check the consistency of the system of equations

Let's check the consistency of the system of equations:

AX = B

[2 -3] K 5[x y] = [1 7]

2x - 3y + K5y = 1

K ≠ 5/3, otherwise the system of equations will be inconsistent.

Step 5: Final Answer

To have a unique solution, the value of K must satisfy the following conditions:

K ≠ 0 and K ≠ 5/3

Therefore, the value of K for which the equation has a unique solution is any real number except 0 and 5/3.

Answer

Answer

Maybe 16/3.......Am I right?

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