Final answer:
The system of equations given has one solution because the lines have different slopes and are therefore not parallel, indicating they will intersect at exactly one point.
Step-by-step explanation:
The question asks how many solutions the system of equations has. The given system is:
To find the number of solutions, we need to determine if these lines intersect. If they do, they will have one solution; if they are the same line, they will have an infinite number of solutions; if they are parallel and distinct, they will have no solutions.
In this case, the lines are not parallel and have different slopes; therefore, they will intersect at exactly one point. The slope of the first equation is 2; the slope of the second equation is -1. Since the slopes are different (2 versus -1), the lines will intersect exactly once, showing that the system of equations has one solution.