Which term(s) describe(s) the system?

3x – 2y = 7
–9x + 6y = –10

dependent
consistent and dependent
consistent and independent
inconsistent

Do you think you could be more specific?

Multiply the first equation by three and add to the second equation.

Observe what you get.

To determine which term(s) describe the given system of equations, we need to analyze the relationship between the two equations.

The first step is to check if the system is consistent or inconsistent. A consistent system means that there is at least one solution that satisfies both equations, while an inconsistent system means there is no solution that satisfies both equations.

Next, we need to determine if the system is independent or dependent. An independent system means that there is a unique solution to the system, whereas a dependent system means that there are infinitely many solutions.

To find out if the system is consistent or inconsistent, we can use any method of solving systems of equations, such as substitution, elimination, or graphing.

Let's solve the system by using the elimination method:

1. Multiply the first equation by 3 and the second equation by -1 to eliminate the variable x:
9x - 6y = 21
9x - 6y = 10

2. Subtract the second equation from the first equation:
9x - 6y - (9x - 6y) = 21 - 10
0 = 11

Since we have obtained an inconsistent equation (0 = 11), the system is inconsistent. This means that there is no solution that satisfies both equations.

Therefore, the correct answer is: inconsistent.