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What are two equations for two lines that will intersect all the time?
Wiki User
∙ 8y ago
They are simultaneous equations.
Wiki User
∙ 8y ago
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When two or more lines intersect at a point they are said to be?
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
What is a solution to a system of equations graphically?
Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.
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.
What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
What lines do not intersect but are on the same plane?
Lines which are parallel. All other lines on the same plane eventually intersect.
What describes all lines that do not intersect?
parallel lines
What do graphs of all equations in the form y equals mx plus b have in common?
They are all lines. Their equations are written in the slope-intercept form, where we clearly can see if they just intersect, or are perpendicular to each other, or parallel, or coincide.
Can the lines of a plane intersect?
All non-parallel lines in a plane will intersect at some point in the plane.
How many ways can two different lines intersect?
It depends on how you define "ways" and how you define "lines" and how you define "intersect" and what kind of geometry you're talking about, but in Euclidean geometry, lines either never intersect, or they intersect at a single point, or they can intersect at all points within the lines.
Two lines that do not intersect are?
Parallel lines will never intersect. They will stay an equal distance apart at all points.
What are the possible solutions for a system of equations?
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
