system of linear equations

Question

Consider the system of linear equations,

x1-6x2 =-27

6x1 + cx2=-157

If this system has no solutions then what is c ? (Hint: use substitution to reduce it to one equation in one variable - then work out how this can fail to lead to a solution for a particular value of )

Answer 1

I would rather work with x and y, so let's make x1 = x and x2 = y

x - 6y = -27

6x + cy = -157

no solutions means the lines are parallel. Rearrange:

6y = x -27 => y = x/6 - 27/6

cy = -6x -157 => y = -6x/c -157/c

equating the gradients (slopes) 1/6 = -6/c => c = -36

This solution ignores the hint. I believe this is easier.