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Linear Equations – Written as Matrix










































System of Linear Equations

A supermarket is selling three different fruits, i.e. apple, orange and pear.

   The price of an apple is RM x, the price of an orange is twice of an apple, and the price of a pear is RM y.

   Two different stalls, stall A and stall B get their supplies from this supermarket.

   Stall A bought 350 apples, 200 oranges and 300 pears and pays RM 680. Stall B bought 400 apples, 150 oranges and 250 pears and pays RM 530.

i) Based on the above information, form a system of linear equations.

ii) Write the above linear equations in the form of a matrix equation


Comments for Linear Equations – Written as Matrix

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Sep 01, 2012
Linear Equations
by: Staff

Answer:


i) Based on the above information, form a system of linear equations.



The price of an apple is RM x

   x = price of an apple

the price of an orange is twice of an apple

   2x = price of an orange

price of a pear is RM y

   y = price of a pear


Summary of prices

   x = price of an apple
   2x = price of an orange
   y = price of pear


Stall A bought 350 apples, 200 oranges and 300 pears and pays RM 680.

    (350 apples)*x + (200 oranges)*2x + (300 pears)*y = 680

   750x + 300y = 680


Stall B bought 400 apples, 150 oranges and 250 pears and pays RM 530.

    (400 apples)*x + (150 oranges)*2x + (250 pears)*y = 530

   400x + 300x + 250y = 530

   700x + 250y = 530



system of linear equations

   750x + 300y = 680

   700x + 250y = 530



ii) Write the above linear equations in the form of a matrix equation


   750x + 300y = 680

   700x + 250y = 530


   │ 750x + 300y │    │ 680 │
   │                    │ = │        │
   │ 700x + 250y │    │ 530 │



   │ 750 + 300 ││ x │    │ 680 │
   │                    ││    │ = │        │
   │ 700 + 250 ││ y │    │ 530 │


Coefficient matrix


   │ 750 + 300 │
   │                  │
   │ 700 + 250 │



Variable matrix


   │ x │
   │    │
   │ y │



Constant matrix



   │680│
   │     │
   │530│



Thanks for writing.

Staff
www.solving-math-problems.com



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