Author: Chicago Public Schools
Last saved by: mike

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                                         SYSTEM OF EQUATIONS-ELIMINATION #4—KEY

Directions:  Solve each system of equations below by eliminating a variable from each system.  In order to 
eliminate a variable, you will have to use multiplication or division to modify both equations.

                                  modified equations                                              modified equations                                               modified equations

1)    4x + 8y = 12    6x +   8y =  52         2)    2x + 3y = 46			        3)    3x - 3y = -15

       3x + 9y = 21    6x + 18y =  72                4x + 6y =   7			               9x + -y = 19

        x =   -5           y =    4    		           no solution	                                         x =    3           y =     8    

4)    10x + 1/2y = 16			     5)      x + y = 5			        6)    5x - 8y = -29

         5x + 2y = 29		                        7x + 7y = 35			               3x + 2y = -31

        x =    1           y =    12    		      infinitely many solutions	                x =   -9           y =    -2    

7)    -x + 10y = -63			     8)    6x - 9y = 42			        9)    -x + -y = 6

       10x - 10y = 180		                        2x - 3y = 16			               -x – (-y) = 9

        x =   13           y =   -5    		            no solution	                                      x =  -7.5           y =     1.5    

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