Can a system of linear equations have no solution or infinitely many solutions?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Can a system of linear equations have no solution or infinitely many solutions and how do you differentiate between the two?

If two lines are coincident (i.e. the same line), then they intersect at all points along the line – that is, infinitely many points and hence infinitely many solutions. If two lines are parallel (and non-coincident) then they do not intersect and there is no solution.

How you know if a system of equations has one solution no solutions or infinitely many solutions?

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

How do you tell if a graph has one solution no solution or infinite solutions?

If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

What does it mean when a system has infinitely many solutions?

If the two lines have the same y-intercept and the slope, they are actually in the same exact line. In other words, when the two lines are the same line, then the system should have infinite solutions. It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

How do you know if a linear system has one none or infinitely many solutions?

A linear system has one solution when the two lines comprising the system intersect once. A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ).

Is a system of linear equation with one solution?

A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct. Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems.

What makes an equation have one solution?

From the above examples, we see that the variable x does not disappear after solving & we say that the linear equation will have one solution if it is satisfied by exactly one value of the variable.

When a system has an infinite solution set the system is said to be?

If the system has exactly one, unique solution then it is independent. If the system has infinite solutions, then it is called dependent.

When does a system of linear equations have no solution?

A system of linear equations has no solution if the lines have the same slope but different y-intercepts. For example, the following systems of linear equations will have no solution. We show the slopes for each system with red and the y-intercepts with blue.

How do you know if a system has infinitely many solutions?

A system of linear equations has infinitely many solutions if the lines have the same slope and the same y-intercept. For example, the following systems of linear equations will have infinitely many solutions. Notice how the slope is the same and how the y-intercept is the same.

What does it mean if there are no solutions to systems?

Lastly, if there are no solutions to a system, it means that the two lines represented by the equation are parallel. For example, consider the following equations: #y=3x# (blue) #y=3x+4# (red) As you can see, the two lines are parallel, and will never meet.

Can a system of two equations and two unknowns have no solution?

It is possible for a system of two equations and two unknowns to have no solution (if the two lines are parallel), or for a system of three equations and two unknowns to be solvable (if the three lines intersect at a single point).