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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.
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
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.
What is consistent system?
A consistent system of equations is one in which there is at least one set of values for the variables that satisfies all the equations simultaneously. In graphical terms, this means that the lines or planes represented by the equations intersect at one or more points. A consistent system can be classified as either independent (with a unique solution) or dependent (with infinitely many solutions). In contrast, an inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.
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.
