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A system of equations has infinitely many solutions when the equations represent the same line or plane. In a two-variable scenario, this occurs when both equations can be simplified to the same linear equation, meaning they are dependent. Graphically, this results in overlapping lines. For example, the equations (2x + 3y = 6) and (4x + 6y = 12) represent the same line and thus have infinitely many solutions.
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What is the definition of a system of equations?
A system of equations is a set of two or more equations that share common variables. The solutions to the system are the values of the variables that satisfy all equations simultaneously. Systems can be classified as consistent (having at least one solution) or inconsistent (having no solutions), and they can also be classified based on the number of solutions, such as having a unique solution or infinitely many solutions.
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
How man solutions can a system have?
A system of equations can have three types of solutions: one unique solution, infinitely many solutions, or no solution at all. A unique solution occurs when the equations intersect at a single point, while infinitely many solutions arise when the equations represent the same line or plane. No solution occurs when the equations represent parallel lines or planes that do not intersect. The nature of the solutions depends on the relationships between the equations in the system.
Do all rational equations have one solution?
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
Systems of equations have one solution?
Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
Do all rational equations have solutions?
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
What are inifintly equations?
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
How many solutions does a nonlinear system of equations?
None, one or many - including infinitely many.
What is the definition of a system of equations?
A system of equations is a set of two or more equations that share common variables. The solutions to the system are the values of the variables that satisfy all equations simultaneously. Systems can be classified as consistent (having at least one solution) or inconsistent (having no solutions), and they can also be classified based on the number of solutions, such as having a unique solution or infinitely many solutions.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
How man solutions can a system have?
A system of equations can have three types of solutions: one unique solution, infinitely many solutions, or no solution at all. A unique solution occurs when the equations intersect at a single point, while infinitely many solutions arise when the equations represent the same line or plane. No solution occurs when the equations represent parallel lines or planes that do not intersect. The nature of the solutions depends on the relationships between the equations in the system.
What does a graph with infinitely many solutions look like?
they have same slop.then two linear equations have infinite solutions
Do all rational equations have one solution?
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
Do systems of equations always have one answer?
No. They can have none, one, finitely many or infinitely many.
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
