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No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
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What is infinity many solutions?
Infinity many solutions refers to a scenario in mathematical problems, particularly in equations or systems of equations, where there are countless answers that satisfy the given conditions. This often occurs in linear equations that are dependent, where one equation can be expressed as a multiple or linear combination of another. In such cases, the solutions can form a continuous set, such as a line or a plane in geometry, rather than a finite number of discrete solutions.
What is the relationship between geometry and non-linear equations?
Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.) For example y = mx + b and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution. With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
In algebra what does it mean if a system is independent?
this means you have no more than 5 solutions in a system of equations.
Do all rational equations have a single solution?
Not all rational equations have a single solution but can have more than one because of having polynomials. All rational equations do have solutions that cannot fulfill the answer.
What does it means if there are an infinite number of solutions to a system of equations?
In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others
What is the solution to a linear equation?
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
How many solutions does an consistent and dependent system of equations have?
It has more than one solutions.
What is infinity many solutions?
Infinity many solutions refers to a scenario in mathematical problems, particularly in equations or systems of equations, where there are countless answers that satisfy the given conditions. This often occurs in linear equations that are dependent, where one equation can be expressed as a multiple or linear combination of another. In such cases, the solutions can form a continuous set, such as a line or a plane in geometry, rather than a finite number of discrete solutions.
Can there be more than one point of intersection between the graphs of two linear equations?
Normally no. But technically, it is possible if the two linear equations are identical.
What are linear equtions and simultanions equations?
Linear Equations are equations with variable with power 1 for eg: 5x + 7 = 0 Simultaneous Equations are two equations with more than one variable so that solving them simultaneously
Independent system of two linear equations has an infinite number of solutions?
If the system is for more than two variables there will be an infinite number of solutions since only two of the variables can be determined while the rest will be free to take any value. Also, technically, it does not matter what the system is independent of. What matters is that the linear equations are independent of one another.
What is the relationship between geometry and non-linear equations?
Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.Non-linear equations represent shapes other than straight lines.
Can a system of linear equations have two solutions?
No. The graph of each linear equation is a straight line, and two or more lines can't all intersect at more than one point. * * * * * Unless all the lines are, in fact, the same line. In that case each point on the line is a solution. That is, there are infinitely many solutions.
What are the linear systems?
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Can you solve system of equations by graphing?
Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.
