
The x y-coordinate plane is given. There are 2 lines on the graph.
The first line labeled 3x + y = 7 enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7, passes through the point (2, 1), crosses the x-axis at approximately x = 2.33, and exits the window in the fourth quadrant.
The second line labeled x + 2y = 4 enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 2, passes through the point (2, 1), crosses the x-axis at x = 4, and exits the window in the fourth quadrant.
(x, y) = 

 
  



To find the solution to the system of equations represented by the lines, we need to solve for the intersection point of the two lines:

1. First line: \( 3x + y = 7 \)
2. Second line: \( x + 2y = 4 \)

Since both lines pass through the point \((2, 1)\), we can verify this by plugging \(x = 2\) and \(y = 1\) into both equations and checking if the equations hold true.

### Step 1: Substitute \(x = 2\) and \(y = 1\) into the first equation:
\[
3(2) + 1 = 7
\]
\[
6 + 1 = 7 \quad \text{(True)}
\]

### Step 2: Substitute \(x = 2\) and \(y = 1\) into the second equation:
\[
2 + 2(1) = 4
\]
\[
2 + 2 = 4 \quad \text{(True)}
\]

Since the point \((2, 1)\) satisfies both equations, the intersection point of the two lines is \((2, 1)\).

Thus, the solution to the system of equations is:
\[
(x, y) = (2, 1)
\]

Would you like more details on how to solve systems of equations, or do you have any other questions?

### Related questions:
1. How can you solve a system of linear equations using substitution?
2. What are other methods to solve systems of linear equations, such as elimination or graphing?
3. How can we determine if two lines are parallel or perpendicular?
4. How do we find the slope of a line given an equation in standard form?
5. What is the significance of the point of intersection between two lines?

### Tip: 
When solving systems of equations graphically, the intersection point of the lines represents the solution, if it exists. If the lines are parallel, there is no solution (the system is inconsistent).

The x y-coordinate plane is given. There are 2 lines on the graph. The first line labeled 3x + y = 7 enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7, passes through the point (2, 1), crosses the x-axis at approximately x = 2.33, and exits the window in the fourth quadrant. The second line labeled x + 2y = 4 enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 2, passes through the point (2, 1), crosses the x-axis at x = 4, and exits the window in the fourth quadrant.

Learn how to find the intersection point of two linear equations: 3x + y = 7 and x + 2y = 4. This detailed guide explains how to solve systems of linear equations graphically and algebraically. Suitable for Grades 9-11, this problem highlights key concepts in algebra and coordinate geometry.

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