Question Type 3: Checking whether the system of linear equations has no solution, one solution or infinite number of solutions Exercises

Determine whether the system of equations $x + y + z = 6$, $2x - y + 3z = 14$, and $3x + y + 4z = 20$ has no solution, one solution, or infinitely many solutions.

Find the general solution to the following system of equations. Hence, determine the number of solutions.

Determine whether the system of equations $x + 2y + 3z = 1$, $2x + 4y + 6z = 2$, and $3x + 6y + 9z = 3$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $2x - y + z = 5$ and $4x - 2y + 2z = 11$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $x + y = 2$ and $2x + 2y = 4$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $x + 2y = 5$ and $2x - y = 1$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $3x + y - z = 4$ and $6x + 2y - 2z = 8$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $x + y = 2$ and $2x + 2y = 5$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $x + y = 1$ and $x + y + z = 3$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $3x + y - z = 4$ and $6x + 2y - 2z = 9$ has no solution, one solution, or infinitely many solutions.

Determine whether the system of equations $x - y = 1$ and $2x - 2y = 3$ has no solution, one solution, or infinitely many solutions.

Solve the following system of equations: