I need help on how to do this

Mathematics

1 answer:

Leni [432]2 years ago

5 0

9514 1404 393

Answer:

see attached

Step-by-step explanation:

a) A system of equations has no solutions when the graphs of those equations do not intersect. If the equations are equations of a line, then the lines must be parallel in order for them not to intersect.

Any parallel line will do.

b) There is one solution when the graphs intersect in exactly one point.

Any line that crosses the one shown will do.

c) There are infinite solutions when the graphs describe the same curve.

A line overlapping the one shown is the one you want.

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A) The inverse of the statement is the opposite. The statement stated that if two lines do not intersect, they are parallel. So, the opposite would be if two lines intercept, they are parallel. This inverse statement is false because, that is not true. Parallel lines mean they never intercept, not if they intercept its parallel.

b) Converse means to engage or explain, I think…so, the converse of the statement would be that yes, it is true that when two lines do not intercept then they are parallel. Because parallel lines never cross or meet, meaning they will NEVER ever have a crossing point.

c) the contrapositive of the statement would be: if two lines do not cross then they are parallel. If they do intercept, then they are not parallel. As simple as that. I think contrapositive means that…I looked what contrapositive means…so I think I’m right.

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I attached a photo showing all the steps including the final answer.