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To solve this system of equations by graphing:

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

The solution to this system is the point where the two lines intersect.

1. Since both equations are set equal to \( y \), we can set them equal to each other:
   \[
   5x - 6 = 2x - 6
   \]

2. Solving for \( x \):
   \[
   5x - 2x = -6 + 6
   \]
   \[
   3x = 0
   \]
   \[
   x = 0
   \]

3. Substitute \( x = 0 \) back into either equation to find \( y \):
   \[
   y = 5(0) - 6 = -6
   \]

So, the solution to the system is:
\[
(0, -6)
\]

Would you like more details or have any questions?

Here are some related questions to explore:
1. How would the solution change if the slopes of the equations were different?
2. How can we verify this solution graphically?
3. What is the significance of the intercept in these equations?
4. How do we interpret the system if the lines are parallel?
5. What if we used substitution instead of setting equations equal?

**Tip:** Graphing systems of equations visually helps confirm algebraic solutions and provides insights into their intersections.

Solve this system of equations by using graphing:
y = 5x - 6
y = 2x - 6

Learn how to solve the system of linear equations y = 5x - 6 and y = 2x - 6 by graphing. This tutorial covers key algebraic concepts like slope-intercept form, setting equations equal, and interpreting intersections. Suitable for students in Grades 8-10.

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