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When solving a linear system algebraically how do you know when there is no solution?
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In solving a system of two linear equations or two functions by graphing what is meant by if the system is consistent or inconsistent?
A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
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 a linear system with infinitely many solution?
It is a system in which the solution set is a straight line.
When solving a system of linear inequalities what does the region that is never shaded represent?
It represents the solution set.
How does graphing a linear system help you verify the results of solving a linear system algebraically?
You see the point the two lines cross, if they do. This is the solution to the system since it is the values of (x,y) that are on both lines The solution is a sytems is those points, if any, (x,y) that satisfy both equations. That is the same as saying they are on both lines. If you graph the equations, this is the same as saying the points that are in the intersection of the lines. This is why parallel lines represent a system with no solution and if two equations are the same line there is an infinite number of solutions.
In solving a system of two linear equations or two functions by graphing what is meant by if the system is consistent or inconsistent?
A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
What is inconsistent system of linear equation?
It is a system of linear equations which does not have a solution.
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 the advantages or disadvantages of solving system of linear equation by graphing?
The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra. The main disadvantage is that your answer will be approximate due to having to read the answer from a graph. Where the solution are integer values, this might be alright, but if you are looking for an accurate decimal answer, this might not be able to be achieved. Another disadvantage to solving linear equations by graphing is that at most you can have two unknown variables (assuming that you are drawing the graph by hand).
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
What is a linear system with infinitely many solution?
It is a system in which the solution set is a straight line.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What is independent system?
Independence:The equations of a linear system are independentif none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
