https://file.aiquickdraw.com/mathbot/file/172619671680184k79lea.jpg

In the image, you are working on a system of equations and verifying whether a given point is a solution to both equations.

### System of Equations:
\[
\begin{cases}
y = x - 3 \\
x - 4y = 6
\end{cases}
\]

You are verifying if the point \((4, 1)\) is a solution:
- For the first equation: \( y = x - 3 \), you substitute \(x = 4\) and \(y = 1\):
  \[
  1 = 4 - 3
  \]
  This is true, so the point \((4, 1)\) satisfies the first equation.

- For the second equation: \(x - 4y = 6\), you substitute \(x = 4\) and \(y = 1\):
  \[
  4 - 4(1) = 6 \implies 4 - 4 = 0
  \]
  This is false since \(0 \neq 6\), so the point \((4, 1)\) does **not** satisfy the second equation.

Thus, the point \((4, 1)\) is **not** a solution to the system of equations because it only satisfies one of the two equations.

---

Now, you are asked to figure out if the point \((-3, 5)\) is a solution to the following system of equations:
\[
\begin{cases}
y = x - 3 \\
x - 4y = 6
\end{cases}
\]
Would you like help with this one?

### Questions to think about:
1. How do we determine if a point is a solution to a system of equations?
2. What happens if a point satisfies one equation but not the other?
3. Can a system have no solution? If so, under what conditions?
4. What are some methods to solve systems of equations besides substitution?
5. What is the graphical interpretation of finding the solution to a system of equations?

#### Tip: Always check each equation in the system when verifying a potential solution.

Is the point (4, 1) a solution to the system of equations y = x - 3 and x - 4y = 6?

Determine if the point (4, 1) is a solution to the system of equations y = x - 3 and x - 4y = 6. Learn how to verify solutions by using the substitution method and check both equations.

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