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To solve the given system of equations for \(a\) and \(b\), let's go through the solution step by step:

### Given Equations:
1. \(18 = 2a + 10\)
2. \(3a = b + 2\)

### Step 1: Solve for \(a\)
From the first equation:
\[
18 = 2a + 10
\]

Subtract 10 from both sides:
\[
8 = 2a
\]

Divide by 2:
\[
a = 4
\]

### Step 2: Solve for \(b\)
Substitute \(a = 4\) into the second equation:
\[
3(4) = b + 2
\]

Simplify:
\[
12 = b + 2
\]

Subtract 2 from both sides:
\[
b = 10
\]

### Final Solution:
\[
a = 4, \, b = 10
\]

Would you like a detailed explanation of any step? Here are some related questions:

1. How do you solve systems of equations using substitution?
2. What other methods can solve a system of linear equations?
3. Can these equations be graphed to verify the solution?
4. How do you check the solution of a system of equations?
5. What is the elimination method for solving equations?

**Tip:** Always check your solution by substituting back into the original equations to ensure it satisfies both!

Use the two equations below to solve for a and b.
18 = 2a + 10
3a = b + 2

Learn how to solve the linear system of equations 18 = 2a + 10 and 3a = b + 2 using the substitution method. This step-by-step guide covers core algebraic concepts and is suitable for students in Grades 7-9.

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