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A system of equations has infinitely many solutions when the equations represent the same line or plane in a coordinate space, meaning they are dependent and consistent. This typically occurs when one equation can be derived from the other through multiplication or addition of constants. In graphical terms, the lines or planes coincide, leading to an infinite number of intersection points.
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How many solutions can a system of linear equations with two variables?
None, one 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.
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.
Two lines intersect how many solutions does the system of equations have?
When two lines intersect, the system of equations has exactly one solution. This solution corresponds to the point of intersection, where both equations are satisfied simultaneously. If the lines are parallel, there would be no solutions, and if they coincide, there would be infinitely many solutions.
How many solutions will a system have if a graph of the solution is coinciding lines?
If a system of equations is represented by coinciding lines, it has infinitely many solutions. This occurs because every point on the line satisfies both equations, meaning that there are countless points that are solutions to the system. In this case, the two equations represent the same line in the coordinate plane.
Can a system of linear equations in two variables have infinitely solutions?
Yes.
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 many solutions does a nonlinear system of equations?
None, one or many - including 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.
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
A system of two linear equations has infinitely many solutions if?
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
How do you know when an algebraic equation has infinitely many solutions?
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
When solving a system of equations by elimination you find what?
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
