https://file.aiquickdraw.com/mathbot/file/1726718483720ec0dddwe.jpg

The system of equations shown in the image is:

\[
\begin{cases}
x - 2y = 9 \\
y = x - 3
\end{cases}
\]

To solve this system of equations, we can use substitution. Here's the step-by-step solution:

1. From the second equation, \( y = x - 3 \).
2. Substitute this expression for \( y \) into the first equation:

\[
x - 2(x - 3) = 9
\]

3. Simplify the equation:

\[
x - 2x + 6 = 9
\]

\[
-x + 6 = 9
\]

4. Solve for \( x \):

\[
-x = 9 - 6
\]

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

5. Now substitute \( x = -3 \) back into the second equation to find \( y \):

\[
y = -3 - 3 = -6
\]

So, the solution to the system is \( x = -3 \) and \( y = -6 \).

Let me know if you'd like more details or have any questions!

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Here are 5 related questions to explore:
1. What is the graphical interpretation of this system of equations?
2. How would you solve the system using the elimination method?
3. What happens if we change the second equation to \( y = x + 3 \)?
4. How do we determine if a system of linear equations has no solution or infinitely many solutions?
5. How would the solution change if the coefficient of \( y \) in the first equation was different?

**Tip:** In systems of equations, substitution is useful when one equation is already solved for one variable!

Solve the system of equations: x - 2y = 9 and y = x - 3.

Learn how to solve the system of linear equations x - 2y = 9 and y = x - 3 using the substitution method. This detailed step-by-step guide explores key algebraic concepts, making it ideal for students in Grades 8-10.

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