Determine whether the following system is consistent or inconsjstent. If the system is consistent, determine whether the equations are dependent or independent. Do not solve the system. \[ \left\{\begin{array}{l} y=-4 x+5 \\ y=5 x+7 \end{array}\right. \] Choose the correct answer below. A. The given system is consistent and independent. B. The given system is inconsistent. c. The given system is consistent and dependent.

Step 1 ：The given system of equations is: \(y = -4x + 5\) and \(y = 5x + 7\)

Step 2 ：To determine whether the system is consistent or inconsistent, we need to check if there is at least one solution that satisfies both equations.

Step 3 ：Setting the two equations equal to each other, we get: \(-4x + 5 = 5x + 7\)

Step 4 ：Solving for x, we get: \(9x = -2\) which simplifies to \(x = -\frac{2}{9}\)

Step 5 ：Substituting \(x = -\frac{2}{9}\) into the first equation, we get: \(y = -4(-\frac{2}{9}) + 5 = \frac{8}{9} + 5 = \frac{53}{9}\)

Step 6 ：Substituting \(x = -\frac{2}{9}\) into the second equation, we get: \(y = 5(-\frac{2}{9}) + 7 = -\frac{10}{9} + 7 = \frac{53}{9}\)

Step 7 ：Since the values of y are the same for both equations, the system is consistent.

Step 8 ：To determine whether the equations are dependent or independent, we need to check if one equation can be obtained from the other by multiplication or addition.

Step 9 ：In this case, the two equations cannot be obtained from each other by multiplication or addition, so the equations are independent.

Step 10 ：\(\boxed{\text{The given system is consistent and independent.}}\)