Maria's Math Web page
(help and tips for algebra II)

 
 

solving linear equations

          An equation is a statement that says two expressions are equal.  A linear equation           only has one variable (such as "x") and the solution will be a number(s) that will make the statement true when substituted

            STEPS FOR SOLVING A LINEAR EQUATION
                    ex:  5x - 10 = 15   write the given linear equation
                       5x = 25   you want to strive to get the "x" alone, so you are going to combine like variables (which would be the 10 and 15) to get the remaining equation
                       x = 5   the last step to completely isolate the variable is to divide both sides by 5 which leaves you with the solution x = 5.  now substitute your answer in to check your work

          TRY ONE ON YOUR OWN!!
   ***( hint: remember to use order of operations!)***

7x + 7= 2(x + 1)


          ANSWER:

7x + 7= 2(x + 1)

                                                                                  7x + 7= 2x + 2
                                                                                       - 7         -7

                                                                                       7x= 2x - 5
                                                                                     -2x    -2x

                                                                                      5x= -5
                                                                                        5      5

                                                                                       x= -1
 
 

solving literal equations

           Literal equations are equations that have more than one variable and are solved for a specific variable in terms of the other variables. *** You will not get a numerical answer ( it will be a variable )***

            STEPS FOR SOLVING A LITERAL EQUATION
                2x - 4y = 8  solve for "y"     write the equation as given
              -4y = 8 - 2x     subtract the 2x in order to isolate the 4y (remember, the key is to get the "y" by itself)
                y = 8/-2 + -2/-4      divide the -4 that remains with the "y" by 8 and -2x. next you will want to simplify your answer.
                y = 1/2 - 2      answer for literal equation

        TRY ONE ON YOUR OWN!!

d = rt
(solve for t)





       ANSWER

d = rt
r      r

d/r = t
 

3 equations for a line

       There are two things that are included in the equation of a line, they are the slope and the "y" intercept.  When identifying and writing the equation of a line, there are three that you must know.
 

                    POINT SLOPE FORM

                       y - y1 = m ( x - x1 )  ----  In this form, m = slope and x1, y1  = a point co-ordinate on the line (could possibly be the y intercept)

                   Y INTERCEPT FORM

                         y = mx + b  ----  Again in this form, m = slope, but b = the y intercept

                   STANDARD FORM

                    ax + by = c  ----  In this form, a/b = the slope, and b/c = the y intercept
 

            TRY SOME ON YOUR OWN!!
            ** identify the form of the line that is being represented.**

                      ex. 2x + 3y = 14 ---- standard form



                1.  y = 4x + 0 ---- ?
                2.  y - 2 = 1/3( x - 3) ---- ?
                3.  0x + 1y = 15 ----?
 

               ANSWERS

               1. y intercept form
                2. point slope form
                3. standard form



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