Identify the type of system of equations and solve the system of equations if possible.9𝑥−3𝑦=327𝑥−9𝑦=21Select the type of system and most correct meaning below.Group of answer choicesAn inconsistent system; the parallel lines will never cross so there is no solution.An inconsistent system; there is really only one line so any of the infinite number of points on that line is a solution.An independent system; the lines will cross in only one place so there is only one solution.A dependent system; the parallel lines will never cross so there is no solutionA dependent system; there is really only one line so any of the infinite number of points on that line is a solution.

First, let's identify the type of system of equations. We have two linear equations:

1. 9x - 3y = 32
2. 7x - 9y = 21

We can simplify these equations by dividing the first equation by 3 and the second equation by 7:

1. 3x - y = 10.67
2. x - 1.29y = 3

These are two different lines, so it's not a dependent system (which would be the same line). They are not parallel lines either, so it's not an inconsistent system. Therefore, it's an independent system.

Now, let's solve the system of equations. We can use the substitution or elimination method. I'll use the substitution method:

First, isolate 'x' in the second equation:

x = 1.29y + 3

Now, substitute 'x' in the first equation:

3(1.29y + 3) - y = 10.67 3.87y + 9 - y = 10.67 2.87y = 1.67 y = 1.67 / 2.87 y = 0.58

Substitute 'y' in the second equation to find 'x':

x = 1.29*0.58 + 3 x = 4.25

So, the solution to the system of equations is x = 4.25 and y = 0.58. This means the lines will cross in only one place. Therefore, the correct answer is:

An independent system; the lines will cross in only one place so there is only one solution.