we know that
A system of three linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions.
If a system has at least one solution, it is said to be consistent
If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line
in this problem we have
x + y + z = 6---------> equation 1
3x + 3y + 3z = 18------> equation 2
-2x − 2y − 2z = -12--------> equation 3
if in the equation 2 divides by 3 both sides
3x + 3y + 3z = 18-------> x + y + z = 6------> equation 2 is equal to equation 1
if in the equation 3 divides by -2 both sides
-2x − 2y − 2z = -12-------> x + y + z = 6------> equation 3 is equal to equation 1
so
equation 1, equation 2 and equation 3 are the same
therefore
the system of equations has infinite solutions
Is a Consistent and Dependent System