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Can the solution of a system of linear inequalities be the points on a line?
yes
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
which graph shows the solution to the system of linear inequalities y>2x+1 y?
3
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.
When solving a system of linear inequalities what does the region that is never shaded represent?
It represents the solution set.
What consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
What is the set of two or more inequalities?
A set of two or more inequalities is known as a system of inequalities. This system consists of multiple inequalities that involve the same variables and can be solved simultaneously to find a range of values that satisfy all conditions. Solutions to a system of inequalities are often represented graphically, where the feasible region indicates all possible solutions that meet all the inequalities. Such systems are commonly used in linear programming and optimization problems.
Why are systems of linear inequality so important?
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
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.
Can the solution of a system of linear inequalities be the points on a line?
yes
Is it possible for a system of two linear inequalities to ha a single point as a solution?
yes it is possible for a system of two linear inequalities to have a single point as a solution.
How is solving a system of linear equations the same as solving a system of linear inequalities?
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 asx + 2y ≤ 3 and x + 2y ≥ 3
When is it possible for a system of two linear inequalities to have no solution?
A system of two linear inequalities can have no solution when the inequalities represent parallel lines that do not intersect. This occurs when the lines have the same slope but different y-intercepts. In such cases, there is no set of values that can satisfy both inequalities simultaneously, resulting in an empty solution set.
When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
When we graph a system of two linear inequalities any point in the doubly shaded region has coordinates that contain both inequalities?
In a graph of a system of two linear inequalities, the doubly shaded region represents the set of all points that satisfy both inequalities simultaneously. Any point within this region will meet the criteria set by both linear inequalities, meaning its coordinates will fulfill the conditions of each inequality. Consequently, this region illustrates all possible solutions that satisfy the system, while points outside this region do not satisfy at least one of the inequalities.
