Question

For what value of k the system of linear equations has a unique solution x+y+z = 2, 2x + y - z = 3 and 3x + 2y +kz= 4

Answer 1

x+y+z=2..... eqn 1

2x+y-z=3.....eqn 2

Add both

therefore,3x+2y=5...... eqn 3

3x+2y+kz=4......eqn 4

Substitute eqn 3 in eqn 4

therefore, 5+kz=4

kz = -1

k=-1/z

Answer 2

For unique solution value k = -1

Given:

x+y+z = 2,    2x + y - z = 3   and 3x + 2y +kz= 4

To find:

What value of k the system of linear equations has a unique solution.

Explanation:

For unique solution value of the equation value of x , y ,z are only one.

x+y+z = 2        ...........................1

2x + y - z = 3      ......................2

3x + 2y +kz= 4     ....................3

Add Equation 1 and 2 We get

3x + 2y = 5

Put this value on Equation 3

3x + 2y +kz= 4

        5 + kz= 4

             k = 4-5 = -1

For unique solution value k = -1

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