Question

the system of equations 3x+4y = 14; kx+7y = 12; and 5x- 6y = 2k are consistent then what is the value of k?​

Answer 1

The condition for the set of equations to be consistent is:

a1/a2 ≠ b1/b2

Given set of equations:

3x+4y = 14 ...........(1)

kx+7y = 12 ..........(2)

5x- 6y = 2k  ...............(3)

considering (1) and (2)

3/k ≠ 4/7

k ≠ 21/4

considering (2) and (3)

k/5 ≠ 7/-6

k ≠ 35/-6

For the system of equations to be consistent, the value of k is real numbers except 21/4 and 35/-6