Solve the following systems of linear equations and determine if they are consistent and independent: 4(vii) 2x + 5y = 17, 5x + 3y = 14; 4(viii) 3x − 5y − 10 = 0, 6x − 10y = 20

For a system $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$:
Here, $a_1 = 2, b_1 = 5$ and $a_2 = 5, b_2 = 3$.

Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ ($\frac{2}{5} \neq \frac{5}{3}$), the system has a unique solution.
Therefore, the system is consistent and independent.

The solution is $\boxed{x=1, y=3}$. The system is consistent and independent.

4(viii)
The given system of equations is:

1. $3x - 5y - 10 = 0 \implies 3x - 5y = 10$
2. $6x - 10y = 20$

For a system $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$:
Here, $a_1 = 3, b_1 = -5, c_1 = 10$ and $a_2 = 6, b_2 = -10, c_2 = 20$.

Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, the system has infinitely many solutions.

It is not independent because the two equations represent the same line.
Therefore, the system is consistent but not independent.

The system has infinitely many solutions and is consistent but dependent.