Solucionario Calculo Una Variable Thomas Finney Edicion 9

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Methods of Solving Linear Equations Linear equations are equations with one unknown, or X, that have an equation that is linear. They are also called first-order linear equations. Solving linear equations is the process of finding the values of the unknowns that make an equation true. There are many methods to solve linear equations, but most are either unreliable or require too many steps. Method 1: Addition or Substitution This method requires that you know how to solve for one variable. You simply choose one variable and set it equal to zero, then use algebraic manipulation to find the other variable  as  well  as  the  answer  to  the  equation. For example, to find the value of X for this equation: with "y" and "x" variables: Substitute the values of "y" and "x": Finally, add all three terms: Readily available evaluation tables let you determine the value of each variable by plugging in numbers into the equation. Evaluation tables can be found at any time and anywhere you can find a simple calculator. Some problems like these involve solving both sides of an equation for one variable and finding another variable from that solution. Other problems require finding a third equation that tells you how to solve for the unknowns. Method 2: Multiplication or Division This method uses the value of one variable to determine the value of another. The process for this method starts by subtracting one variable from the other. If the second variable is positive, take its square root. If it is negative, take its reciprocal, which is called a reciprocal square root. The table below shows how many times each number appears in each quadrant of both variables. For example, in this problem, "y" has a value of -1 and "x" has a value of 3; therefore, you would want to look up numbers in the tables that list numbers less than or equal to -1 and greater than 3. There are tables that cover all possible values of both variables. In this example, all values greater than -1 and less than 3 appear in the table. Square roots will yield answers of positive or negative numbers, so you must take your answers and add them to the answers from each variable in order to get a final answer for the unknowns ("y" and "x"). It is a simple process, but it can become tedious if there are many unknowns. This method also requires that you know how to evaluate or find the value of each variable. You would use either a method to find one variable from another, such as by evaluating an equation, or by using a table that gives exact values for both variables. eccc085e13