What is an example of infinitely many solutions?
An infinite solution has both sides equal. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.
How do you know if a solution has infinitely many solutions?
We can identify which case it is by looking at our results. If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
How do you know how many solutions a system has?
If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
What does it mean to have infinite solutions?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. No Solution Equations.
When a system has 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 does infinitely many mean?
“Infinitely many” means that there are not finitely many. In other words, “infinitely many” means that there does not exist some real integer n such that you can describe the objects with a set of cardinality (size) n.
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.
How can you tell how many solutions a system has?
A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
Is infinitely many solutions consistent?
Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .
Do parallel lines have infinitely many solutions?
When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.
How can you tell how many solutions an equation has?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
How do you know if there are infinitely many solutions on a graph?
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. When the lines intersect, the point of intersection is the only point that the two graphs have in common.
How do I know how many solutions a system has?
Which systems of equations have infinite solutions?
Which systems of equations have infinite solutions? An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
When does system have infinite solutions?
The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. In other words, when the two lines are the same line, then the system should have infinite solutions. Moreover, the question is what indicates when the system has no solution one solution or infinite solutions?
What does infinitely many solutions mean?
One Solution,No Solution,or Infinitely Many Solutions – Consistent&Inconsistent Systems
What are examples of equations with no solutions?
Multiply equation 1 by 4