5x+6y+7z=178 6x+4y+2z=124 3x+3y+3z?

We have 5x+6y+7z=178; 6x+4y+2z=124.

Now with the option

(a)  3x+3y+3z=60, we get,

-x+z=58, and 3x-3z=66, hence we donot get a solution for this.

(b)

3x+3y+3z=62.5, we get,

-x+z=53, and 3x-3z=61, hence we donot get a solution for this.

(c)

3x+3y+3z=90, we get,

-x+z=-2, and 3x-3z=6, hence we get using x=1, y=22, z=-1

(d) we have found the solution, and that is the part (c).