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A linear equation corresponds to a line, and a linear inequality corresponds to a region bounded by a line.
Consider the equation y = x-5.
This could be graphed as a line going through (0,-5), (1,-4), (2,-3), and so on. The inequality y > x-5 would be the region above that line.
What else can I help you with?
Why is it important the linear equations and inequalities?
There are many simple questions in everyday life that can be modelled by linear equations and solved using linear programming.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
How are linear inequalitys differant from linear equations?
Inequalities have greater than, less than, greater than or equal to, or less than or equal to signs. Equations have an equal sign.
How are linear inequalities different from linear equations?
A linear equation represents a line. A linear inequality represents part of the space on one side (or the other) of the line defined by the corresponding equation.
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 makes linear inqualities and an linear equation the same?
Linear inequalities and linear equations are similar in that both involve linear expressions and use the same variables in a linear format. They can be represented graphically, where linear equations depict straight lines, while linear inequalities represent regions of the coordinate plane. Additionally, both types of mathematical statements can be solved using similar algebraic techniques, though solutions for inequalities often involve ranges of values rather than specific points. Ultimately, they both express relationships between variables, but inequalities include a relational aspect (greater than or less than) that equations do not.
Why is it important the linear equations and inequalities?
There are many simple questions in everyday life that can be modelled by linear equations and solved using linear programming.
How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
How can you use coordinate graphs to solve linear equations and linear inequalities?
To solve it by coordinate graphs you would take a point from the line and plug in the X and Y value into the equations and or inequalities.
How are functions and linear equations similar?
Linear equations are a small minority of functions.
What types of equations or inequalities describe points x y that lie on a circle?
Linear equations or inequalities describe points x y that lie on a circle.
Are their similar things about inequalities and equations?
They both have variables.
How are the rules for solving inequalities similar to those for solving equations?
Solving inequalities and equations are the same because both have variables in the equation.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
How do you differentiate linear inequalities in two variables from linear equations in two variables?
Linear inequalities in two variables involve expressions that use inequality symbols (such as <, >, ≤, or ≥), while linear equations in two variables use an equality sign (=). The solution to a linear equation represents a specific line on a graph, while the solution to a linear inequality represents a region of the graph, typically shaded to show all the points satisfying the inequality. Moreover, linear inequalities allow for a range of values, whereas linear equations specify exact values for the variables.
How are linear inequalitys differant from linear equations?
Inequalities have greater than, less than, greater than or equal to, or less than or equal to signs. Equations have an equal sign.
What is the difference between the solution of a system of linear inequalities and the solution of a system of linear equations?
The solution of a system of linear equations consists of specific points where the equations intersect, typically yielding a unique point, infinitely many points, or no solution at all. In contrast, the solution of a system of linear inequalities represents a region in space, encompassing all points that satisfy the inequalities, often forming a polygonal shape in two dimensions. While equations define boundaries, inequalities define areas that can include multiple solutions. Thus, the nature of their solutions differs fundamentally: precise points versus expansive regions.
