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One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent.
If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent.
If the graph of the equations is the same line, the system has infinitely simultaneous solutions.
We can use several methods in order to solve the system algebraically.
In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example,
2x + 3y = 6
4y + 6y = 12
These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system.
Try to solve this system of equations,
2x + 3y = 6
4x + 6y = 7
If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations).
When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
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How do you know if a point is a solution to a system of equations?
The coordinates of the point satisfy each of the equations.
Is linear algebra and linear equations the same?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
How do you know if an equation is linear?
You know if an equation is linear if it is a straight line. You can also know if the equation is y = mx + b where there are no absolute values nor exponents.
How do you find a solution for a linear equation?
Solution can be found by using three methods: 1. Cross Multiplication Method 2. Substitution Method 3. Elimination Method Other Method can also be there but I don't know You can further get info about these method by searching these on Google Search.
How do you know when a relationship is a linear function?
It is in a strait line.
What is a solution of a linear equation called?
Ordered Pair * * * * * An ordered SET. There can be only one, or even an infinite number of variables in a linear system.
How do you know which region of the graph of a system of linear inequalities contains the solutions?
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
What is the application for rank of the matrix?
Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
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.
How do you know when an equation has a unique solution?
You know when an equation has a unique solution when there is only one variable in it. (APOLOGIES)(RESPONSE: the question was categorized under "Linear Algebra". x^2 is non-linear and is thus not allowed, nor are sin x, x^3, log x, 2^x, etc etc. However, you are correct if you consider non-linear equations. Unfortunately, I am not sure there is a method to determine the number of solutions to non-linear equation.)If there are more than one variable, each variable over the first will be free, and give you infinite solutions - with each additional variable adding another dimension to your solution.(RESPONSE: See above response with regards to this topic being categorized under "Linear Algebra". My statement is true in Linear Algebra. Furthermore, Row Reduced Echelon Form and augmented matrices are the most fundamental concepts in Linear Algebra. Under normal circumstances, I would agree with you. However, this question was categorized under "Linear Algebra", so I presumed that the person asking the question is a college student.)In general, you know that a system of equations has a unique solution when the row reduced echelon form of the augmented matrix has a pivot position in every column, except for the right most column which is the solution. If you do not have an augmented matrix, then the RREF will have a pivot position in every column.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
What is the symbol of linear meters?
Since a linear metre is the same as a metre, the symbol is m
Is coffee a mixture a compound or a solution?
It is a solution if you would have done your science homework you would know this.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
Explain why a system of linear equations cannot have exactly two solutions?
if you can fart out of your chin then you know your headin in the right direction
How do you know if a point is a solution to a system of equations?
The coordinates of the point satisfy each of the equations.
How do you covert 100 feet into linear feet?
100 Feet IS 100 Linear Feet. If you wanted to know how many linear feet would give you 100 square feet, you would take the square root of 100, which is 10... SO a 10 x 10 linear foot area would be 100 square feet, and a 100 x 100 Linear foot area would be 10,000 square feet.
