Home MATHEMATICS TOPIC 8: LINEAR PROGRAMMING ~ MATHEMATICS FORM 4

TOPIC 8: LINEAR PROGRAMMING ~ MATHEMATICS FORM 4

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MATHEMATICS FORM FOUR NOTES ALL TOPICS

TOPIC 8: LINEAR PROGRAMMING ~ MATHEMATICS FORM 4

Simultaneous Equations
Simultaneous Equation from Word Problems
Form simultaneous equation from word problems
LINEAR PROGRAMMING.
Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit.
  • It gives the best way of utilizing the scarce resources available.
  • It is so called because it only involves equations and inequalities which are linear.
Simultaneous Equation.
One
of the methods used in solving linear simultaneous equations is a
graphical method. Two linear simultaneous equations in two unknowns can
be graphically solved by passing through the following procedures.
  1. Draw
    the two lines which represent the two equations on the xy – plane this
    is done by deter mining at least two points through which each line
    passes, the intercept are commonly used
  2. Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations.
FACT:
  • If two straight lines are not parallel then they meet at only one point:
  • In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations.
Example 1
Graphically solve the following system of simultaneous equations.
46 1444210273845
47 1444210317344
Example 2
Find the solution to the following system of simultaneous equations by graphical method.
48 1444210563949
49 1444210606695
50 1444210667982
Solving Simultaneous Equations Graphically
Solve simultaneous equations graphically
Example 3
Solve the following simultaneous equations graphically and check your solution by a non-graphical method:
51 1444210923465
52 1444210955374
Example 4
Find the solution to the following system of simultaneous equations by graphical method.
48 1444210563949
49 1444210606695
50 1444210667982
Exercise 1
Find the solution to the following systems of simultaneous equations graphically.
53 1444211296420
Try:
Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the
same market and paid 24 shillings for 16 oranges and 18 mangoes. What
was the price for a mango and for an orange?

 

 

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