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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.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
What is the purpose of linear inequalities?
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Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
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 consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
Why are linear equation and linear inequalities not solved in the same manner?
Although there are similarities, the solutions to a linear equation comprise all points on one line: a one-dimensional object. The solutions to a linear inequality comprise all points on one side [or the other] of a line: a two-dimensional object.
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.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
What is the purpose of linear inequalities?
asdfghjkldfghjklhjkl
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
How are linear equations and linear inequalities similar?
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.
Why do you clear decimals when solving linear equations and inequalities and example?
Even if you keep the decimal, later on you will still have to remove it. It is just an easier way to solve the equation.
Inequalities containing two inequality symbols are called what?
Linear inequalities in one variable
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
