Pairs of straight Lines

GRAPH SKETCHING 20040301


                                             (matrix) (x,y)   =         (values)

1/(determinant) *(inverse) (matrix) (x,y) = 1/(determinant) *(inverse)*(values)

For each pair of equations, sketch both lines on one pair of axes, AND solve using matrices to see if the intersection is correct.


Three questions form a homework: these should take around ten minutes each.


Remember to label your axes, intersects and lines (I’ll accept a and b, where a is the top one and b is the bottom of each pair). Remember to give the position of your intersection – and THEN use the matrix methods to see how well the two systems work. The idea is to use one system to help support the other.


1   x  –  3y = 9                                             4    3x + 5y = 15
     2x + 4y = 8                                                   4x – 3y = 12


2    2x + 3y = 6                                            5     x + 2y   = -6
      x   –  4y = 8                                                 2x + 3y   = +6


3     2x – 3y = 12                                          6     6x –   y = 12
       –x + 4y = 12                                                 4x – 3y = 12


The instructions for graph sketching methods were given on sheet 20060810 “Sketching straight lines” in this series and the matrix method for solving these was explained on sheets 20040118 and 20040203 Algebra.



unchecked:
1   x=5.1, y=1                               4  x=  105/29, y=72/29
2   x=48/11, y=-10/11                  5  x=  30, y=6
3  x=72/5, y=36/5                        6  x=  12/5, y=6/5



© David Scoins 2017