Linear and simultaneous equations

Question

Draw the graph of y=2x-5 for -3 less than or equal to Xmas less than or equal to 5. Also, draw the graphs of the following pairs of simultaneous equations on the same axes for -4 less than or equal to x less than or equal to 4. 

 

1) x +y=2 and 2x - y=-5

2)2x+y=0 and 3x-2y=7 

3)5x-2y=-4 and -3x+y=3

4)x+y=4 and 4x + 2y=11

5)Hence, solve each pair of simultaneous equations graphically.

Answer 1

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1)  y = 2-x 

      2x - (2-x) =-5

       2x - 2 + x = -5 

        3x - 2 = -5

        3x  = -3

         x = -1

        y = 2 - -1 = 3

 

2)  y = -2x

     3x - 2(-2x) = 7

       3x + 4x = 7

      7x = 7

      x=1

       y = -2

 

 

 3)   y = 3 + 3x

        5x - 2(3 + 3x) = -4

        5x - 6 - 6x = -4

          -x - 6 = -4

            -x = 2

              x = -2

          y = 3 + 3(-2) = 3 + -6 = -3

           

 4)  y = 4 - x

         4x + 2(4-x) = 11

            4x + 8 - 2x = 11

            2x + 8 = 11

             2x = 3

            x = 3/2

           y = 4 - 3/2 = 8/2 - 3/2 = 5/2

 

             4(3/2) + 2(5/2) = 12/2 + 10/2 = 22/2 = 11