https://file.aiquickdraw.com/mathbot/file/1726069851704wk94u8zc.jpg

The image shows a system of linear equations solved graphically, with two intersecting lines. The equations appear to be as follows:

1. \( p + q = 13 \)
2. \( 0.01p + 0.25q = 1.57 \)

The solution to the system of equations is at the point where the two lines intersect, which is marked on the graph as \( (7, 6) \). This means that:
- \( p = 7 \)
- \( q = 6 \)

We can confirm this by substituting \( p = 7 \) and \( q = 6 \) into both equations:

1. For \( p + q = 13 \):
   \[
   7 + 6 = 13
   \]
   This is true.

2. For \( 0.01p + 0.25q = 1.57 \):
   \[
   0.01(7) + 0.25(6) = 0.07 + 1.5 = 1.57
   \]
   This is also true.

Thus, the solution \( p = 7 \) and \( q = 6 \) satisfies both equations.

Would you like more details on solving systems of equations graphically or algebraically? Here are some related questions you may explore:

1. How do you solve a system of equations algebraically using substitution?
2. What are the steps to solve a system of equations using the elimination method?
3. Can you explain the meaning of the slope and intercepts in the graph of each equation?
4. How do we determine whether a system of equations has one solution, no solution, or infinitely many solutions?
5. What is the difference between consistent and inconsistent systems of equations?

**Tip:** When solving systems of linear equations graphically, the point of intersection is the solution to both equations.

Solve the system of equations graphically: p + q = 13 and 0.01p + 0.25q = 1.57.

Explore the graphical solution of the system of linear equations p + q = 13 and 0.01p + 0.25q = 1.57. Learn how to find the intersection point of the lines representing these equations to determine the solution (p, q) = (7, 6). Suitable for students in Grades 8-10.

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