Maths homework problem (Sets of linear equations)?

Question

Find the value of c for which the system of equations: 

5x+2y =3 
2x+3y-5z =1 
cx-5y+15z = c 

does not have a unique solution. 

Apparently the solution is c=4 but I m not sure how to come about this answer.. Any help would be massively appreciated

Answer 1

The equations are 5x + 2y = 3, 2x + 3y - 5z = 1 and cx - 5y + 15z = c

Write the equations into matrix form AX = B.

Where A is coefficient matrix, X is variable matrix and B is constant matrix.

The system does not have a unique solution means the system has no solution.

Equate detA  = 0

40 - 10c  = 0

40 = 10c

c  = 40/10

c  = 4

The value of c  = 4.