Question
How many solutions does this system of equations have?
Responses
None
None
Infinitely many
Infinitely many
Exactly one
Exactly one
Exactly two
Exactly two
Graph of a system of linear equations. Equation 1 is 3x plus 2y equals 6. Equation 2 is negative 4x plus 5y equals 15. The graphs intersect at a point.
Responses
None
None
Infinitely many
Infinitely many
Exactly one
Exactly one
Exactly two
Exactly two
Graph of a system of linear equations. Equation 1 is 3x plus 2y equals 6. Equation 2 is negative 4x plus 5y equals 15. The graphs intersect at a point.
Answers
GPT-4o mini
The system of equations you described has **exactly one** solution.
In a system of linear equations, if the graphs of the equations intersect at a single point, that means the equations are consistent and independent. Thus, there is one unique solution represented by the coordinates of that intersection point.
So based on the given information, the correct response is **Exactly one**.
In a system of linear equations, if the graphs of the equations intersect at a single point, that means the equations are consistent and independent. Thus, there is one unique solution represented by the coordinates of that intersection point.
So based on the given information, the correct response is **Exactly one**.