System A
Line 1: $y=-\frac{2}{3} x+4$
Line 2: $2 x+3 y=12$
This system of equations is:
inconsistent
consistent dependent
consistent independent
This means the system has:
a unique solution
Solution: $(\square, \square)$
no solution
infinitely many solutions

Step 1 ：We are given the system of equations: Line 1: \(y=-\frac{2}{3} x+4\) and Line 2: \(2 x+3 y=12\)

Step 2 ：We need to determine if the system is inconsistent, consistent dependent, or consistent independent. This will tell us if the system has a unique solution, no solution, or infinitely many solutions.

Step 3 ：The system of equations is given by two lines. If the lines intersect at a single point, the system is consistent independent and has a unique solution. If the lines are parallel and do not intersect, the system is inconsistent and has no solution. If the lines coincide, the system is consistent dependent and has infinitely many solutions.

Step 4 ：To determine which case we have, we can compare the slopes and y-intercepts of the two lines. The slope and y-intercept of the first line are given directly. For the second line, we can rearrange the equation to the form \(y = mx + b\) to find the slope and y-intercept.

Step 5 ：The slopes of the two lines are equal, which means the lines are either parallel or the same line. Since the y-intercepts are also equal, the lines coincide.

Step 6 ：Therefore, the system of equations is consistent dependent and has infinitely many solutions.

Step 7 ：Final Answer: The system of equations is \(\boxed{\text{consistent dependent}}\) and has \(\boxed{\text{infinitely many solutions}}\).