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How many solutions did this linear system have?
To determine how many solutions a linear system has, we need to analyze the equations involved. A linear system can have one unique solution, infinitely many solutions, or no solution at all. This is usually assessed by examining the coefficients and constants of the equations, as well as using methods like substitution, elimination, or matrix analysis. If the equations are consistent and independent, there is one solution; if they are consistent and dependent, there are infinitely many solutions; and if they are inconsistent, there are no solutions.
The three quantities of solution linear equations?
The three quantities of solution for linear equations are consistent, inconsistent, and dependent. A consistent system has at least one solution, either unique or infinitely many. An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect. A dependent system has infinitely many solutions, indicating that the equations represent the same line in different forms.
How many solution does a linear inequality in one variable have?
Inequalities tend to have infinitely many solutions.
How do you find the linear system if you know its solutions?
You cannot since there are infinitely many sets of lines that can pass through any single point - the solution.
If a system of linear of linear equations has infinitely many solutions what does this mean about the two lines?
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
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.
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
Can a linear system have exactly two solutions?
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
How many solutions did this linear system have?
To determine how many solutions a linear system has, we need to analyze the equations involved. A linear system can have one unique solution, infinitely many solutions, or no solution at all. This is usually assessed by examining the coefficients and constants of the equations, as well as using methods like substitution, elimination, or matrix analysis. If the equations are consistent and independent, there is one solution; if they are consistent and dependent, there are infinitely many solutions; and if they are inconsistent, there are no solutions.
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
The three quantities of solution linear equations?
The three quantities of solution for linear equations are consistent, inconsistent, and dependent. A consistent system has at least one solution, either unique or infinitely many. An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect. A dependent system has infinitely many solutions, indicating that the equations represent the same line in different forms.
How many solutions are there to a linear inequality?
Infinitely many. The solution space is part of a plane.
How many solution does a linear inequality in one variable have?
Inequalities tend to have infinitely many solutions.
How do you find the linear system if you know its solutions?
You cannot since there are infinitely many sets of lines that can pass through any single point - the solution.
If a system of linear of linear equations has infinitely many solutions what does this mean about the two lines?
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
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 many solutions can a system of linear equations with two variables?
None, one or infinitely many.
