They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.

How many solutions is it possible for a system of linear equations to have?

one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel

Why cant a system of linear equations cannot have exactly two solutions?

Because linear lines can't intersect in two seperate places. They either intersect at one specific coordinate, or the lines are on top of each other and they intersect at every point.

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.

How many solutions will a system of equations have if the graphs of the lines intersect?

A system of equations will have one solution if the graphs of the lines intersect. This is because the lines intersect at a single point. Let's say that point is (a, b). The x = a, y = b is the one and only solution for the system.

What is true about the lines represented by this system of linear equations?

That they, along with the equations, are invisible!

In solving a system of two linear equations or two functions by graphing what is meant by if the system is consistent or inconsistent?

A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.

What are the linear systems?

A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

When is system of linear inequalities have no solution?

When the lines never intersect, usually when they are parallel.

What is true about a system of two linear equations that has no solution?

The two equations represent parallel lines.

What system of equations has no solution?

A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.

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.

How many solutions can two lines have that intersect once?

Since the lines that intersect are the equations, if they intersect once they have one solution.

If a system of linear equations has exactly one solution then the two lines are what?

perpendicular

If there is no solution to a system of equations it means?

extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.

Can a linear system have exactly two solutions?

NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).

What are two equations for two lines that will intersect all the time?

They are simultaneous equations.

What is the situation when two linear inequalities have no common solution?

To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).

Why does the intersection of the two lines represent the solution of the linear equation system?

The solution to a system is an ordered pair (x,y) where the two lines intersect.

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 type of lines are y equals 2x and y equals 4x plus 2?

Those two statements are linear equations, not lines. If the equations are graphed, each one produces a straight line. The lines intersect at the point (-1, -2).

What are the three types of possible solutions to a system of equations?

If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.

What types of lines would be the result of an inconsistent system of equation?

If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.

When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?

When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..