The problem asks to select the correct statement about the solution to a system of equations, and then to describe the system of equations. The available options for the solution are: A. The solution is $(-9, 7)$. B. There are infinite solutions. C. There is no solution. The available options to describe the system are: The equations are dependent (identical graphs), the equations are inconsistent (parallel lines), or the equations are independent and consistent (graphs intersect at one point).
2025/3/13
1. Problem Description
The problem asks to select the correct statement about the solution to a system of equations, and then to describe the system of equations. The available options for the solution are: A. The solution is . B. There are infinite solutions. C. There is no solution. The available options to describe the system are: The equations are dependent (identical graphs), the equations are inconsistent (parallel lines), or the equations are independent and consistent (graphs intersect at one point).
2. Solution Steps
From the given choices, we know that the system has exactly one solution, . Therefore, the graphs of the two equations intersect at exactly one point. Such a system is called "independent and consistent".
Independent equations have different slopes.
Consistent equations have at least one solution.
3. Final Answer
The solution to the system is .
The equations are independent and consistent. Their graphs intersect at one point.