# How do you tell if there are infinitely many solutions on a graph?

## How do you tell if there are infinitely many solutions on a graph?

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.

**How do you tell if a system of linear equations has infinitely many solutions?**

If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.

### How do you tell if a graph is independent dependent or inconsistent?

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 .

**How do you find 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.

## What system of linear equations that has infinitely many solutions and their graphs coincide?

dependent system

A dependent system has infinitely many solutions. The lines are coincident. They are the same line, so every coordinate pair on the line is a solution to both equations.

**How do you know if a solution is infinite?**

Well, there is a simple way to know if your solution is infinite. 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 can you tell how many solutions a system of linear equations have?

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.

**How many solutions are there of the graph is coinciding?**

If the graph lines for equations coincide there are infinitely many solutions.

## Which system type is a linear system with infinitely many solutions?

**How many solutions does a consistent independent system have?**

one solution

A consistent system of equations has at least one solution, and an inconsistent system has no solution.

### What are 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.

**How do you write infinitely many solutions as an ordered pair?**

Both ways of writing the solution give the same ordered pairs. In Method 1, you pick a value for y and find the corresponding x value. In Method 2, you pick a value for x and find the corresponding y value. Since the values you pick can be anything, this gives the infinite number of ordered pairs that solve the system.

## What is a linearly independent solution?

Linearly independent solutions can’t be expressed as a linear combination of other solutions. If f (x) and g (x) are nonzero solutions to an equation, they are linearly independent solutions if you can’t describe them in terms of each other. In math terms, we’d say that and is no c and k for which the expression is true.

**How do you graph a linear system with infinite solutions?**

When we graph a linear system with infinite solutions, we will get two lines that overlap. That is, they intersect at every point on the line, since the two equations are equivalent and give us the same line. Let’s take a look at some examples to see how this can happen.

### How do you know if a graph is linearly independent?

Using a Graph to Find Linearly Independent Solutions One way of determining whether a set of solutions is linearly independent is to graph them. If they are linearly independent, they will cross at exactly one place. Linear dependent solutions will either be parallel to each other or turn out to be actually the same line.

**When is a set linearly independent?**

A set X of elements of V is linearly independent if the corresponding family {x}x∈X is linearly independent. The trivial case of the empty family must be regarded as linearly independent for theorems to apply. A geographic example may help to clarify the concept of linear independence.