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Let's solve the system of equations using the elimination method:

We are given the following system of equations:
1. \( 3x + 2y = 18 \)
2. \( x + 5y = 19 \)

### Step 1: Multiply the second equation to align the \(x\)-terms.
We want to eliminate \(x\), so let's multiply the second equation by 3 to align the coefficients of \(x\):
\[
3(x + 5y) = 3(19)
\]
This simplifies to:
\[
3x + 15y = 57
\]

Now, we have the system:
1. \( 3x + 2y = 18 \)
2. \( 3x + 15y = 57 \)

### Step 2: Subtract the first equation from the second to eliminate \(x\):
\[
(3x + 15y) - (3x + 2y) = 57 - 18
\]
Simplifying this gives:
\[
13y = 39
\]
Solve for \(y\):
\[
y = \frac{39}{13} = 3
\]

### Step 3: Substitute \(y = 3\) into one of the original equations (let's use \(x + 5y = 19\)) to find \(x\):
\[
x + 5(3) = 19
\]
\[
x + 15 = 19
\]
\[
x = 19 - 15 = 4
\]

### Final Solution:
The solution to the system is \( x = 4 \) and \( y = 3 \).

The ordered pair is \( (4, 3) \).

Would you like further details or explanations on any part? Here are some related questions:

1. How do you determine which variable to eliminate first?
2. What if the coefficients of \(x\) or \(y\) were already aligned?
3. How would the solution method change if you had fractions in the system?
4. Can this system be solved using substitution instead of elimination?
5. How would you solve this system graphically?

**Tip:** In elimination, it's important to align coefficients of one variable so that subtracting or adding the equations cancels it out easily.

Solve the system using elimination.
3x + 2y = 18
x + 5y = 19

Learn how to solve the system of linear equations 3x + 2y = 18 and x + 5y = 19 using the elimination method. This detailed step-by-step solution demonstrates key algebraic concepts such as multiplying and subtracting equations to eliminate variables. Suitable for students in Grades 9-10.

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