Question

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

A. Always
B. Sometimes
C. Never
I think it is A but I am not sure and it is impossible for system of equations with different slopes and different y-intercepts to be parallel or infinite.

Answer 1

Always. The only time you have 0 solutions is when you have two parallel lines, meaning same slope. The only time you have more than 1 is when you have the SAME line, because every point is a answer. Therefore, when you have two completely different lines, then they MUST only have 1 solution always.

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Answer 2

The answer is :
A. Always


Also
If two equations have different slopes but equivalent y-intercepts, they will have one solution and that will be the point where the y-intercept is. If two equations have different slopes and different y-intercepts, then there will be one solution where those two lines meet. If two equations have the same slope but different y-intercepts, the lines will be parallel, and there is no possible intersection point. And if two equations have equal slopes and equal y-intercepts, these lines will have an infinite amount of solutions, because if the equations are one the same line, every single point on that line is a solution to the system.