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                      I. Model Problems.  
                        II. Practice 
                    III. Challenge Problems 
                      VI. Answer Key 
                            
                            
         
                       Web Resources 
                            
                     Systems of Linear Equations 
            www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/ 
                            
                  Interactive System of Linear Equations: 
         www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/interactive-
                    system-of-linear-equations.php 
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                      I. Model Problems 
         
        You can solve systems of linear equations by graphing, the elimination 
        method, or by substitution. 
         
        To solve by graphing, graph both of the linear equations in the system. 
        The solution to the system is the point of intersection of the two lines. 
        It’s best to use the graphing approach when you are given two lines in 
        slope-intercept form. 
         
        Example 1 Solve the system by graphing. 
              y = 2x + 5 
              y =  1 x 1 
                2
                  
        Graph the equations: 
                                         
        The lines intersect at the point (-4, 3).  
         
        The solution is x = -4, y = 3 or (-4, 3). 
         
         
                
                
               It’s best to use the elimination method when equations can easily be 
               added or subtracted to eliminate one of the variables. To use the 
               elimination method, add the equations together to “eliminate” one of 
               the variables. Solve the remaining equation, which will have only one 
               variable. Substitute the value of the variable into one of the original 
               equations to get the value of the variable you eliminated. 
                
               Example 2 Solve the system by elimination: 
                          -6x – 10y = -14 
                          4x + 10y = 6 
                
               Notice that if you add the equations together, you can eliminate y and 
               solve for x. 
                    6x10y 14                  Add the equations together to 
                                                  eliminate y. 
                    4x10y 6         
                    2x  8
               x = 4                              Divide each side by -2 to solve for 
                                                  x. 
               4(4) + 10y = 6  16 + 10y = 6      Substitute x = 4 into the second 
                                                  equation to solve for y. 
               10y = -10                          Subtract 16 from each side. 
               y = -1                             Divide each side by 10. 
                
               The solution is x = 4, y = -1, or (4, -1). 
                
               It’s best to use the substitution method when one equation is solved 
               for one variable in terms of the other. Substitute this expression into the 
               other equation and solve the resulting equation. Substitute the value 
               into one of the original equations to find the value of the other variable. 
                
               Example 3 Solve the system by substitution: 
                          -2x + 4y = 30 
                          y = 3x + 10 
                
                
                
                 
                Notice that the second equation gives the value of y in terms of x, so if 
                can be substituted into the first equation. 
                -2x + 4(3x + 10) = 30               Substitute y = 3x + 10 into the first 
                                                    equation. 
                10x + 40 = 30                       Simplify. 
                10x = -10                           Subtract 40 from each side. 
                x = -1                              Divide each side by 10. 
                y = 3(-1) + 10                      Substitute x = -1 into the second 
                                                    equation to solve for y. 
                y = 7                               Simplify. 
                 
                The solution is x = -1, y = 7, or (-1, 7).