Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable. By : Manish Yadav For better understanding

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Independent and Dependent Variables Independent Variables Independent variables are variables that you put into the equations Dependent Variables Dependent variables are variables that you solve for

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Just as common sense would dictate. If something is independent, then it is on its own. But if it is dependent, then it relies on someone or something else. A dependent variable relies on what is used in place of the independent variable

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y = 2x - 4 Using the equation above, y has to be the variable Why ? Because it is the variable that is being solved for Dependent

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Because linear equations have two variables,there are many possible combinations of answers Those possible solutions are written as ordered pairs. Usually an ordered pair is written with the independent variable first then the dependent variable

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Example: y = 3x - 5 Because we solved for y, then x is the independent variable The ordered pair would then be written as ( x , y )

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If we do not know which variable is independent, then we choose one. No matter which one is independent, we will still produce similar ordered pairs ( r , s ) is similar to ( s , r ) Not congruent/equal

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Most of the time when we use the variables x & y in an equation, x is independent and y is dependent There are some exceptions, but we will work with those at a much later time

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As said before, there are many possible ordered pairs To find more than one solution, we use a Table of Values x y 2 3 -2 1 0 -3

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Class Examples: 2a + b = 4 3r - 2s = 7 2 + x = y

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