https://file.aiquickdraw.com/mathbot/file/172424584899338tj43jj.jpg

Yes, I can help with that!

From the image, the problem is asking for the point where the two lines intersect. The system of linear equations given is:

\[
2x - y = 6
\]
\[
y = 5x
\]

To find the point of intersection, we need to solve these two equations simultaneously.

### Step 1: Substitute the second equation into the first.
Since \( y = 5x \), we can substitute \( y \) in the first equation:

\[
2x - (5x) = 6
\]

### Step 2: Simplify the equation.
\[
2x - 5x = 6
\]
\[
-3x = 6
\]

### Step 3: Solve for \( x \).
\[
x = \frac{6}{-3} = -2
\]

### Step 4: Substitute \( x = -2 \) back into the second equation to find \( y \).
\[
y = 5(-2) = -10
\]

### Solution:
The point of intersection is \( (-2, -10) \).

Would you like more details or have any other questions about this process?

### Related Questions:
1. How do you verify if the solution \((-2, -10)\) is correct?
2. Can you graphically represent the solution on a coordinate plane?
3. What would happen if both lines were parallel?
4. Can the substitution method be used for all systems of linear equations?
5. How does this solution change if the second equation were \(y = 5x + 1\)?

### Tip:
When solving systems of equations, always ensure that both equations are in a comparable form before solving, which can help avoid errors.

Learn how to solve a system of linear equations using the substitution method. Detailed step-by-step solution for the equations 2x - y = 6 and y = 5x, finding the intersection point (-2, -10). Suitable for high school students.

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