Systems of equations with different slopes and different y-intercepts have more than one solution.
A. Always
B. Sometimes
C. Never
I think it's B.
I really need some help...
@ANONYMOUS
If they are linear equations, it is A.
Parallel lines (same slope) never intersect. But lines with different slopes must intersect somewhere.
You're correct! The correct answer is B. Sometimes.
When you have a system of equations with different slopes and different y-intercepts, there are three possible scenarios:
1. The lines intersect at a single point, which means there is one unique solution to the system of equations. This occurs when the lines have different slopes and different y-intercepts.
2. The lines are parallel, which means they never intersect. In this case, there is no solution to the system of equations. This occurs when the lines have the same slope but different y-intercepts.
3. The lines are coincident, which means they are essentially the same line and intersect at infinitely many points. In this case, there are infinitely many solutions to the system of equations. This occurs when the lines have the same slope and the same y-intercept.
So, when the lines have different slopes and different y-intercepts, the system of equations can have one unique solution, no solution, or infinitely many solutions. Since it can have multiple solutions in some cases, the answer is sometimes, which corresponds to option B.