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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.
When equations of linear systems have different slopes how many solutions does it have?
One solution
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
In the graph of a linear inequality the shaded region above or below the line is called?
The shaded region above or below the line in the graph of a linear inequality is called the solution region. This region represents all the possible values that satisfy the inequality. Points within the shaded region are solutions to the inequality, while points outside the shaded region are not solutions.
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Do solutions to systems of linear inequalities need to satisfy linear inequalities?
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.
How many solution sets do systems of linear inequalities have. Must solutions to systems of linear inequalities satisfy both inequalities. In what case might they not?
There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.
How are the graphs of systems of linear equations and inequalities related to their solutions?
The graphs of systems of linear equations represent the relationships between variables, with each line corresponding to an equation. The point(s) where the lines intersect indicate the solution(s) to the system, showing where the equations are satisfied simultaneously. For systems of linear inequalities, the graphs display shaded regions that represent all possible solutions that satisfy the inequalities; the intersection of these regions highlights the feasible solutions. Therefore, both the graphs and their intersections are crucial for understanding the solutions to the systems.
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 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.
When equations of linear systems have different slopes how many solutions does it have?
One solution
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
Do solutions to systems of linear inequalities need to satify both inequalities?
If it is joined by an "and" it does. If it is joined by an "or" it does not.
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
