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To solve the system of equations graphically, we need to plot both equations on the coordinate plane and find the point where they intersect.

### The system of equations is:
1. \( x + y = 7 \)
2. \( x - y = 3 \)

#### Step 1: Rearrange the equations to slope-intercept form (i.e., \( y = mx + b \)).
- **For the first equation**: \( x + y = 7 \)
  \[
  y = -x + 7
  \]
  This is a straight line with slope \( -1 \) and y-intercept \( 7 \).

- **For the second equation**: \( x - y = 3 \)
  \[
  y = x - 3
  \]
  This is a straight line with slope \( 1 \) and y-intercept \( -3 \).

#### Step 2: Plot the lines
- The first line \( y = -x + 7 \) has a negative slope and crosses the y-axis at \( 7 \).
- The second line \( y = x - 3 \) has a positive slope and crosses the y-axis at \( -3 \).

#### Step 3: Find the intersection point
The intersection of these two lines will give the solution to the system.

To solve algebraically, set the two equations equal to each other:
\[
-x + 7 = x - 3
\]
Solving for \( x \):
\[
7 + 3 = 2x \quad \Rightarrow \quad 10 = 2x \quad \Rightarrow \quad x = 5
\]
Now, substitute \( x = 5 \) into either equation to find \( y \):
\[
5 + y = 7 \quad \Rightarrow \quad y = 2
\]

Thus, the solution is \( (5, 2) \).

Would you like me to provide a detailed graphical plot for this system, or do you have any questions?

### Related Questions:
1. What is the slope of the line \( x + y = 7 \)?
2. How can we interpret the intersection point of two lines graphically?
3. What happens when two lines are parallel in a system of linear equations?
4. Can we solve this system using substitution or elimination methods?
5. How do you determine the slope from a linear equation?

### Tip:
Always check your graphical solution by substituting the coordinates of the intersection back into both original equations to ensure accuracy.

Solve the following linear system graphically. x + y = 7, x - y = 3

Learn how to solve the linear system of equations x + y = 7 and x - y = 3 graphically. This problem involves key algebraic concepts such as linear equations, slope-intercept form, and graphing. Suitable for students in Grades 8-10.

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