Solve this system of equations. x + y + z = 6 3x + 3y + 3z = 18 -2x − 2y − 2z = -12

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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions