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Why do some systems of equations have one solution?
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.
The two lines graphed below are parallel How many solutions are there to the system of equations?
Although there is no graph, the number of solutions is 0.
Two distinct lines that do not intersect are parallel?
2 lines the same width apart are parallel.
How many pairs of parallel sides does a quadrilateral have?
A quadrilateral has 4 sides, 2 in which never intersect. Therefore, the lines that don't intersect are called parallel. There are 4 parallel sides but has 2 pairs of parallel sides.
What are perpedicular lines?
Perpendicular lines are like two strangers standing at a right angle to each other - they never meet and have nothing in common. They are a pair of lines that intersect at a 90-degree angle, creating a perfect L-shape. Think of them as the odd couple of geometry - they may not get along, but they sure know how to keep things interesting.
