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To solve this system of equations by elimination, let's go through the steps:

The system given is:
\[
6x + y = 18
\]
\[
-6x + 4y = 12
\]

### Step 1: Add the Equations
Since the coefficients of \( x \) are \( +6 \) and \( -6 \), we can eliminate \( x \) by adding the two equations:

\[
(6x + y) + (-6x + 4y) = 18 + 12
\]

This simplifies to:
\[
0x + 5y = 30
\]
or simply:
\[
5y = 30
\]

### Step 2: Solve for \( y \)
Divide both sides by 5:
\[
y = \frac{30}{5} = 6
\]

### Step 3: Substitute \( y = 6 \) Back into One of the Original Equations
Now that we know \( y = 6 \), substitute this value into the first equation to find \( x \):

\[
6x + 6 = 18
\]

Subtract 6 from both sides:
\[
6x = 12
\]

Then divide by 6:
\[
x = 2
\]

### Solution
The solution to the system is:
\[
(x, y) = (2, 6)
\]

Would you like more details or have any questions?

### Related Questions
1. How do you solve systems of equations using the substitution method?
2. What are other methods for solving systems of equations besides elimination?
3. How can you check if the solution to a system of equations is correct?
4. What is the difference between dependent, independent, and inconsistent systems?
5. How do you graphically interpret the solution of a system of equations?

### Tip
When using elimination, try to set up the equations so that one of the variables cancels out easily by adding or subtracting the equations. This can save time and reduce the complexity of the calculations.

Solve the system of equations using elimination: 6x + y = 18 and -6x + 4y = 12

Learn how to solve the system of equations 6x + y = 18 and -6x + 4y = 12 using the elimination method. This solution provides a step-by-step approach, covering concepts such as adding equations, isolating variables, and substituting back to find the solution.

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