What kind of equation has infinite solutions?
linear equations
A system of linear equations has infinite solutions when the graphs are the exact same line.
What is an infinite solution?
It is possible to have more than solution in other types of equations that are not linear, but it is also possible to have no solutions or infinite solutions. No solution would mean that there is no answer to the equation. Infinite solutions would mean that any value for the variable would make the equation true.
How do you know if a solution is infinite?
Well, there is a simple way to know if your solution is an infinite solution. 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.
Are infinite solutions consistent?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. 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 .
How do you find infinite 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 if a system has infinite solutions?
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.
How can a matrix have infinite solutions?
As you can see, the final row of the row reduced matrix consists of 0. This means that for any value of Z, there will be a unique solution of x and y, therefore this system of linear equations has infinite solutions.
How does a matrix have infinitely many solutions?
Note: To know about the infinite solution of a matrix first we have to check nonzero rows in the matrix. That means if the number of variables is more than nonzero rows then that matrix has an infinite solution.
How do you know if a matrix has infinite solutions?
In simple words, when a system is consistent, and the number of variables is more than the number of nonzero rows in the RREF of the matrix, the matrix equation will have infinitely many solutions.
How do you make a matrix have infinite solutions?
What is infinite solution in system of equations?
A system of equations has infinite solutions when the lines are parallel, i.e. they have the same slope, and they have the same y-intercept. In fact one equation is a scalar multiple of the other and hence, in effect, the equations represent the same line!
What does infinitely many solutions mean?
When an equation has infinitely many solutions, it means that if the variable was turned into a number, the equation would be correct or true, no matter which number or value is placed.
What is infinite number of solutions?
Infinite Solutions. The equation 2 x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. Let’s see what happens when we solve it. We first combine our like terms. We see two x terms that we can combine to make 2 x.
What are infinite solutions?
Infinite Solutions. The first is when we have what is called infinite solutions. This happens when all numbers are solutions. This situation means that there is no one solution. In terms of our treasure hunt, it means that we can’t find the treasure because the location of the treasure can be anywhere. There is no x that marks the spot.