https://file.aiquickdraw.com/mathbot/file/1725807828249ixf9k7g4.jpg

The image contains a set of exercises related to solving systems of linear equations using the elimination method. I will help you with one of these problems and provide detailed steps on how to solve them. Let’s start with the first system in the image:

### Exercise 1: Solve the system using the elimination method
\[
\begin{aligned}
x + 2y &= 3 \\
x - y &= 6
\end{aligned}
\]

#### Step 1: Eliminate one variable
- To eliminate \(x\), we can subtract the second equation from the first.

\[
(x + 2y) - (x - y) = 3 - 6
\]

Simplify the equation:

\[
x + 2y - x + y = -3
\]

\[
3y = -3
\]

#### Step 2: Solve for \(y\)
\[
y = \frac{-3}{3} = -1
\]

#### Step 3: Substitute \(y = -1\) into one of the original equations
We substitute into the first equation:
\[
x + 2(-1) = 3
\]

\[
x - 2 = 3 \quad \Rightarrow \quad x = 5
\]

#### Final solution:
The solution to the system is:
\[
x = 5, \quad y = -1
\]

Would you like me to continue solving other problems from the image, or provide more detailed steps? Let me know if you have questions on this.

Here are 5 related questions for further practice:
1. How do you know when to use the elimination method over substitution?
2. What happens if both variables are eliminated

Solve the system of linear equations using the elimination method. For example: x + 2y = 3 and x - y = 6.

Learn how to solve systems of linear equations using the elimination method, including step-by-step instructions on how to eliminate one variable and solve for the other. Example problem: Solve x + 2y = 3 and x - y = 6.

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