College Algebra CLEP Prep Practice Exam

How many solutions does the system of equations 5x + 4y = 9 and 6x - 3y = 18 have?

1. No solution

2. One solution

3. Two solutions

4. Infinitely many solutions

The correct answer is: One solution

This system of equations has only one unique solution because the two equations represent two distinct lines. The solution is the point where the two lines intersect, and since they are not parallel or coincident, they will only intersect at one point. Option A is incorrect because if the two lines were parallel, there would be no intersection and therefore no solution. Option C is incorrect because, in order for a system of equations to have two solutions, the two lines would have to intersect at two distinct points, which is not the case here. Option D is incorrect because for a system of equations to have infinitely many solutions, the two equations would have to be equivalent, meaning they would represent the same line. This is also not the case for these two equations. Therefore, the only possible solution is one unique solution.