https://file.aiquickdraw.com/mathbot/file/1728062251538k5pntp5w.jpg

The system of equations presented in the image is:

1. \( y = x + 2 \) (red line)
2. \( y = 3x - 2 \) (blue line)

To find the solution, we need to determine the point where the two lines intersect, which represents the solution to the system of equations. Visually, the two lines appear to intersect at the point \( (2, 4) \).

We can verify this by substituting \( x = 2 \) into both equations:

For \( y = x + 2 \):
\[
y = 2 + 2 = 4
\]
For \( y = 3x - 2 \):
\[
y = 3(2) - 2 = 6 - 2 = 4
\]
Both equations give \( y = 4 \), confirming that the point of intersection is indeed \( (2, 4) \).

Thus, the solution to the system is \( (2, 4) \).

Let me know if you need further details or have any questions!

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Here are five related questions to explore further:

1. How do you solve a system of equations algebraically?
2. What does it mean if two lines in a system of equations are parallel?
3. How can you tell if a system of equations has no solution by looking at a graph?
4. What are the different methods for solving a system of linear equations?
5. How can you determine the solution to a system of equations if the lines overlap?

**Tip:** When solving systems of equations graphically, always double-check the coordinates of the intersection point by substituting into both original equations to ensure accuracy.

Find the solution to the system of equations: y = x + 2 and y = 3x - 2.

This page provides a step-by-step explanation on how to find the solution to a system of equations: y = x + 2 and y = 3x - 2. Learn how to use graphing techniques to determine the intersection point of two linear equations, suitable for Grades 7-9.

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