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# What is a graphing system of equations with infinitely many solutions?

## What is a graphing system of equations with infinitely many solutions?

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 result of substitution tells you a system has infinite solutions?

For an answer to have an infinite solution, the two equations when you solve will equal 0=0 .

What does infinite solutions look like?

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 does a systems graph look like if it has an infinite number of solutions?

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 . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

### What does infinite solutions look like 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.

### What type of system has infinitely many solutions?

system of linear equations
A system of linear equations can have no solutions, exactly one solution, or infinitely many solutions. If the system has two or more distinct solutions, it must have infinitely many solutions.

What are infinite solutions examples?

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 tell if a system of equations has no solution or infinitely many?

## How do you know if a solution has no solution or infinite solutions?

Some equations have exactly one solution. In these equations, there is only one value for the variable that makes the equation true. You can tell that an equation has one solution if you solve the equation and get a variable equal to a number.