Question

Systems of equations with different slopes and different y-intercepts have one solution.

a) Always
b) Sometimes
c) Never
d) It depends on the number of equations

Answer 1

Systems of equations with different slopes and different y-intercepts typically intersect at one point, hence generally having one solution. The correct answer to the question is 'sometimes' as there may be exceptions in complex systems of equations.

Step-by-step explanation:

Systems of equations with different slopes and different y-intercepts will generally have one solution. This is because the differing slopes mean that the lines are not parallel, and as long as they are not exactly the same line (which would involve having the same y-intercept), they will intersect at exactly one point. Here, the answer to the question is (b) Sometimes, because while typically different slopes and y-intercepts imply one solution, in the context of more complex systems with more than two equations, other scenarios can occur.