I am a beginner at algebra. I understand the formulas for finding the slopes and solving linear equations. I don't understand all the ins and outs of it, but I do have a good working knowledge of the concepts. What I need is some direction. I have been asked the following question.

Consider a system of linear equations in which the slope of one line is positive and the slope of the other line is negative. Will the system always have a solution? Explain how you know.

I read that horizontal lines do not have a slope and dividing by zero is undefined, but does that mean it is not a negative slope? I could benefit from some clarification on the question, as well.