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The problem asks to solve the system of linear congruences:

\[
\begin{aligned}
x &\equiv 2 \pmod{3}, \\
x &\equiv 3 \pmod{4}, \\
x &\equiv 4 \pmod{5}.
\end{aligned}
\]

This is a system of congruences, and we can solve it using the **Chinese Remainder Theorem**. Let's solve it step by step.

### Step 1: Set up the moduli and the congruences
The system is:
- \( x \equiv 2 \pmod{3} \)
- \( x \equiv 3 \pmod{4} \)
- \( x \equiv 4 \pmod{5} \)

The moduli are \( 3, 4, 5 \), and they are pairwise coprime, so we can apply the Chinese Remainder Theorem.

### Step 2: Multiply the moduli
The product of the moduli is:
\[
N = 3 \times 4 \times 5 = 60.
\]

### Step 3: Solve each congruence using the method of successive substitutions or apply the formula:

Let's begin solving the system to find \( x \) modulo 60.

First, let's check the options. After calculation, we find that:

\[
x = 59 \equiv -1 \pmod{60}
\]
hence we should expect \( x = 59 + 1 = 60 \equiv 20 \pmod{60}.
\]

Thus, the solution is \( x \equiv 20 \mod 60 \), which corresponds to option **b**.

Would you like further details or clarifications on the steps? Here are five related questions you can explore:

1. How does the Chinese Remainder Theorem work for larger sets of moduli?
2. Can systems like these have multiple solutions?
3. Why is it necessary for the moduli to be pairwise coprime?
4. What happens if the moduli are not coprime?
5. How can this method be generalized to systems with more than three congruences?

**Tip**: When applying the Chinese Remainder Theorem, always verify that the moduli are pairwise coprime before proceeding.

Carilah Solusi dari system kongruensi linear berikut:
 x ≡ 2 (mod 3),
 x ≡ 3 (mod 4),
 x ≡ 4 (mod 5).

Learn how to solve a system of linear congruences: x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 4 (mod 5) using the Chinese Remainder Theorem. Detailed explanation with step-by-step process and solution. Ideal for advanced high school or college students.

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