Q: Can 3 lines intersect at only 1 point?

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wrong!

No, they can intersect at infinitely many points.

Line #1 ==> Y = x Line #2 ==> Y = x + 1 These two lines are parallel, have no points in common, and never intersect. (3 ways to say the same thing)

Yes, there are three ways that two different planes can intersect a line: 1) Both planes intersect each other, and their intersection forms the line in the system. This system's solution will be infinite and be the line. 2) Both planes intersect the line at two different points. This system is inconsistent, and there is no solution to this system. However, both planes will still be intersecting the same line, albeit at different locations on the line. 3) Both planes intersect each other, but their intersection does NOT form the line in the system. However, if the line in the system intersects the planes' intersection, then they will all intersect a single point. The solution will be finite and be a single point. There are also 3 ways two different planes WON'T both intersect a line. 1) The two planes and the line are all parallel to each other, and none of them intersect each other. 2) The line is parallel to one plane, but intersects the other plane. 3) The same as #2, but now the line is parallel to the other plane and intersects the one plane.

n+1 = vertices of a pyramid If: n = number of sides of the polygonal base AND a pyramid has 1 point where line segments from points of the polygonal base intersect

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No, that is not true.

they intersect 1 point at a 90 degree angle at all sides

wrong!

Parallel lines don't intersect, no matter how many of them there are.

No, they can intersect at infinitely many points.

Lines don't intersect:- 1) When lines are parallel 2) When lines don't lie on same plane

The only lines that are in the same plane that do not intersect are: 1. Lines of finite length (eg 1 6" line on the floor at one end of the room and another 8" line at the other end) 2. Parallel lines

By a process of elimination and substitution the lines intersect at: (1/4, 0)

Line #1 ==> Y = x Line #2 ==> Y = x + 1 These two lines are parallel, have no points in common, and never intersect. (3 ways to say the same thing)

If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.

they intersect at point (1,-2)

yes or no