Questions: Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 3x - y = 6 x - (1/3)y = 2

Solution Steps

We are given the following system of equations:

\[ \begin{array}{l} 3x - y = 6 \\ x - \frac{1}{3}y = 2 \end{array} \]

To eliminate the fraction in the second equation, multiply the entire equation by 3:

\[ 3(x - \frac{1}{3}y) = 3 \times 2 \]

This simplifies to:

\[ 3x - y = 6 \]

Now, we have the system:

\[ \begin{array}{l} 3x - y = 6 \\ 3x - y = 6 \end{array} \]

Both equations are identical, which means they are dependent.

Since the equations are dependent, the system has infinitely many solutions. The solution set can be expressed in terms of one of the variables.

Final Answer