Question

1. state the solution for each systems of equations.

solution:
solution:
solution:

Explanation:

To solve the problem of identifying the solution for each system of linear equations from their graphs, we analyze each graph based on the intersection of the lines:

First Graph (Top):

Step 1: Identify Intersection

The two lines intersect at a single point. To find the coordinates, we observe the grid. Let's assume the grid has integer coordinates. From the graph, the intersection point appears to be \((x, y) = (4, 2)\) (or similar, depending on grid scale—adjust if needed).

Step 2: Conclusion

A single intersection means one solution at the point of intersection.

Second Graph (Middle):

Step 1: Check Line Relationship

The two lines are parallel (same slope, different y - intercepts). Parallel lines never intersect.

Step 2: Conclusion

No intersection means no solution.

Third Graph (Bottom):

Step 1: Check Line Relationship

The two lines are coincident (same line, same slope and y - intercept). Every point on the line is a solution.

Step 2: Conclusion

Coincident lines mean infinitely many solutions.

Final Answers:

• First Graph: One solution (e.g., \((4, 2)\) – adjust based on exact grid).
• Second Graph: No solution.
• Third Graph: Infinitely many solutions.

(Note: If the grid has specific markings, refine the intersection point. For example, if each grid square is 1 unit, count the units from the origin to the intersection.)

Answer:

To solve the problem of identifying the solution for each system of linear equations from their graphs, we analyze each graph based on the intersection of the lines:

First Graph (Top):

Step 1: Identify Intersection

The two lines intersect at a single point. To find the coordinates, we observe the grid. Let's assume the grid has integer coordinates. From the graph, the intersection point appears to be \((x, y) = (4, 2)\) (or similar, depending on grid scale—adjust if needed).

Step 2: Conclusion

A single intersection means one solution at the point of intersection.

Second Graph (Middle):

Step 1: Check Line Relationship

The two lines are parallel (same slope, different y - intercepts). Parallel lines never intersect.

Step 2: Conclusion

No intersection means no solution.

Third Graph (Bottom):

Step 1: Check Line Relationship

The two lines are coincident (same line, same slope and y - intercept). Every point on the line is a solution.

Step 2: Conclusion

Coincident lines mean infinitely many solutions.

Final Answers:

• First Graph: One solution (e.g., \((4, 2)\) – adjust based on exact grid).
• Second Graph: No solution.
• Third Graph: Infinitely many solutions.

(Note: If the grid has specific markings, refine the intersection point. For example, if each grid square is 1 unit, count the units from the origin to the intersection.)