Is it possible for a system of equations to have an infinite number of solutions?
An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
Is it possible for a system of equations to have all real numbers as solutions?
You arrive at the true statement “3 = 3”. When you end up with a true statement like this, it means that the solution to the equation is “all real numbers”. This equation happens to have an infinite number of solutions. Any value for x that you can think of will make this equation true.
Can a system of equations have more than 2 solutions?
There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.
Is it possible that there are no solutions to a system of two equations in three variables?
For systems of equations in three variables, there are an infinite number of solutions on a line or plane that is the intersection of three planes in space.
When a system has an infinite solution set the system is to be?
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. If a system has no solution, it is said to be inconsistent .
Is it possible for a system of linear equations to have no solutions True or false?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What equation has no solution?
When a problem has no solution you’ll end up with a statement that’s false. For example: 0=1 This is false because we know zero can’t equal one. Therefore we can conclude that the problem has no solution.
Is it possible for a system of two linear equations to have exactly two solutions Why or why not?
Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.) The word unique in this context means there is a solution, and it’s the only one.
What system of equations has no solution?
inconsistent system of equations
An inconsistent system of equations is a system of equations that has no solution.
What are the three possible solutions to a system of equations?
The three types of solution sets: A system of linear equations can have no solution, a unique solution or infinitely many solutions. A system has no solution if the equations are inconsistent, they are contradictory.
Can a system of equations have many equations and many variables?
So a System of Equations could have many equations and many variables. When the number of equations is the same as the number of variables there is likely to be a solution. Not guaranteed, but likely. When there is no solution the equations are called “inconsistent”.
How do you solve a system with no solution algebraically?
Trying to solve a system with no solutions algebraically will lead to a contradiction. Logic requires being familiar with the equations, like being able to recognize parallel lines, to determine that a system has no solution.
What is an inconsistent system of equations?
An inconsistent system of equations is a system of equations with no solution. We can determine if our system is inconsistent in three ways: graphing, algebra, and logic. Graphs of an inconsistent system will have no points of intersection. Trying to solve a system with no solutions algebraically will lead to a contradiction.
How do you know there are infinite solutions to this system?
And since the -intercepts are different, we know the lines are not on top of each other. There is no solution to this system of equations. In other words, the equations are equivalent and share the same graph. Any solution that works for one equation will also work for the other equation, so there are infinite solutions to the system.