The problem is to solve the system of linear equations by graphing. For the given problem (number 6):

The system of equations is:

1. $y = x + 4$
2. $x + y = 6$

Steps to Solve by Graphing:

1. Rewrite both equations in slope-intercept form ($y = mx + b$) if necessary.

   • Equation 1 is already in slope-intercept form: $y = x + 4$.
   • For Equation 2: $x + y = 6$ $y = -x + 6$

2. Graph each equation:

   • For $y = x + 4$:

     • Slope ($m$) = 1, y-intercept ($b$) = 4.
     • Plot the y-intercept (0, 4).
     • Use the slope to find another point (1 unit up, 1 unit right). Second point: (1, 5).

   • For $y = -x + 6$:

     • Slope ($m$) = -1, y-intercept ($b$) = 6.
     • Plot the y-intercept (0, 6).
     • Use the slope to find another point (1 unit down, 1 unit right). Second point: (1, 5).

3. Find the point of intersection:

   • Both lines pass through the point (1, 5).
   • Therefore, the solution to the system is $\boxed{(1, 5)}$.

Would you like me to graph this for visualization? Let me know! 😊

Related Questions:

1. How can you verify the solution of a system of equations algebraically?
2. What does it mean when the lines in a system of equations are parallel?
3. How can you solve a system of equations using substitution instead of graphing?
4. How do slope and y-intercept determine the behavior of a line?
5. What is the significance of the point of intersection in real-world problems?

Tip:

Always check the accuracy of your graph by plugging the intersection point into both equations to verify the solution!