What is an example of infinitely many solutions?
When a problem has infinite solutions, you’ll end up with a statement that’s true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other equation.
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 make 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.
What are infinite solutions?
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.
How do you find infinite solutions?
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.
Is infinitely many 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 .
What is infinitely many solutions on a graph?
When we graph systems of equations, the intersection of the lines is the solution. If a system has infinitely many solutions, then the lines overlap at every point. In other words, they’re the same exact line! This means that any point on the line is a solution to the system.
What is infinitely many solutions in matrices?
Which system of equations has infinitely many solutions?
dependent system
A dependent system has infinitely many solutions. The lines are exactly the same, so every coordinate pair on the line is a solution to both equations.
Can a 3×3 matrix have infinitely many solutions?
A 3×3 matrix equation Ax=b is solved for two different values of b. In one case there is no solution, and in another there are infinitely many solutions.
What is an example of an infinite solution?
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 is the general solution of matrix?
We know that matrix multiplication is linear so we can check out the general solution as follows: A(x h + x p) = Ax h + Ax p = 0 + b = 0. This simply verifies that it is ok to add on the homogeneous solutions and that you still have a “solution” in the literal sense of the word solution.
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?
In general, infinitely many solutions means you can substitute any value for some variable(s) and get infinitely many answers. No solution applies when you can not find any solution to make a relationship true. I can explain further, particularly through the use of systems of equations.