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How is solving a system of linear equations the same as solving a system of linear inequalities?
Wiki User
∙ 11y ago
Not quite sure of the direction of the argument required.
Any inequality can be made into an equality by using an auxiliary variable. For example,
x + 2y < 3 is equivalent to x + 2y - a = 3 where a is some positive variable. [This method is used in linear programming.]
Conversely, any equality can be written as a combination of two inequalities. For example,
x + 2y = 3 is the same as
x + 2y ≤ 3 and x + 2y ≥ 3
Wiki User
∙ 11y ago
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Can a system of equations have more than two inequalities?
A system of equations can have any number of inequalities.
What are the uses of linear inequalities?
In question and answer logic answers are given and if they fall in an area bounded by the inequality then it is a good answer. After graphing three or more inequalities the vertexes are the possible maxima of the system of equations.
What are the solutions to system of inequalities?
Systems of inequalities in n variables with create an n-dimensional shape in n-dimensional space which is called the feasible region. Any point inside this region will be a solution to the system of inequalities; any point outside it will not. If all the inequalities are linear then the shape will be a convex polyhedron in n-space. If any are non-linear inequalities then the solution-space will be a complicated shape. As with a system of equations, with continuous variables, there need not be any solution but there can be one or infinitely many.
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.
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
When solving a system of linear inequalities what does the region that is never shaded represent?
It represents the solution set.
What is a method for solving a system of linear equations in which you multiply one or both equations by a number to get rid of a variable term?
It is called solving by elimination.
Who discovered solving linear system equations by using matrices?
Arthur Cayley
What is the first step in solving a system of nonlinear equations by substitutions?
In general, a system of non-linear equations cannot be solved by substitutions.
Can a system of equations have more than two inequalities?
A system of equations can have any number of inequalities.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
What consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
Why is it the graphing method is the least reliable method in solving system of linear equations?
putang ina nyu
What are the uses of linear inequalities?
In question and answer logic answers are given and if they fall in an area bounded by the inequality then it is a good answer. After graphing three or more inequalities the vertexes are the possible maxima of the system of equations.
How did the system of equations develop?
The system of equations developed from the early days with ancient China playing a foundational role. The Gaussian elimination was initiated as early as 200 BC for purposes of solving linear equations.
What is the relationship between linear algebra and economics?
Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.
What is the advantages or disadvantages of solving system of non-linear equation?
The main advantage is that many situations cannot be adequately modelled by a system of linear equations. The disadvantage is that the system can often get very difficult to solve.
