The given set of equations follows the pattern:

$V_i = 1 + \frac{\sum R}{\text{denominator}}$

where the numerators and denominators involve different combinations of resistances ($R_0, R_1, R_2, R_3, R_4$).

Given equations:

1. $4.47 = 1 + \frac{R_3 + R_2 + R_1 + R_0}{R_4}$
2. $3.16 = 1 + \frac{R_2 + R_1 + R_0}{R_4 + R_3}$
3. $2.24 = 1 + \frac{R_1 + R_0}{R_4 + R_3 + R_2}$
4. $1.58 = 1 + \frac{R_0}{R_4 + R_3 + R_2 + R_1}$

Steps to Solve:

1. Rewrite each equation to isolate the fraction:

   • $\frac{R_3 + R_2 + R_1 + R_0}{R_4} = 4.47 - 1 = 3.47$
   • $\frac{R_2 + R_1 + R_0}{R_4 + R_3} = 3.16 - 1 = 2.16$
   • $\frac{R_1 + R_0}{R_4 + R_3 + R_2} = 2.24 - 1 = 1.24$
   • $\frac{R_0}{R_4 + R_3 + R_2 + R_1} = 1.58 - 1 = 0.58$

2. Express the system of equations in terms of resistances and solve step by step.

Would you like me to proceed with solving for $R_0, R_1, R_2, R_3, R_4$?

Here are 5 related questions for further exploration:

1. How can we solve for individual resistances in a system of linear equations?
2. What is the significance of these resistance ratios in electrical circuits?
3. How does this relate to voltage dividers in circuit analysis?
4. Can this method be applied to other series-parallel resistor networks?
5. How would these values change if an additional resistance was added?

Tip: When solving systems of equations, always try to express one variable in terms of another to simplify substitution.