How many solutions does this system of equations have?

Question

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.

Answer 1

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.