Formation of a System of Linear Equations
The meaning of a system of linear equations can be understood by
formulating a mathematical model of a simple practical problem.
Three persons A, B and C go to a supermarket to purchase same
brands of rice and sugar. Person A buys 5 Kilograms of rice and 3 Kilograms of
sugar and pays ₹ 440. Person B purchases
6 Kilograms of rice and 2 Kilograms of sugar and pays ₹ 400.
Person C purchases 8 Kilograms of rice and 5 Kilograms of sugar and pays ₹ 720.
Let us formulate a mathematical model to compute the price per Kilogram of rice
and the price per Kilogram of sugar. Let x be the price in rupees per
Kilogram of rice and y be the price in rupees per Kilogram of sugar.
Person A buys 5 Kilograms of rice and 3 Kilograms sugar and pays ₹ 440 . So, 5x + 3y = 440 . Similarly, by considering Person B and Person C, we get 6x
+ 2 y = 400 and 8x + 5 y = 720 . Hence the
mathematical model is to obtain x and y such that
5x + 3y = 440, 6x + 2 y = 400, 8x + 5 y = 720 .
In the above example, the values of x and y which
satisfy one equation should also satisfy all the other equations. In other
words, the equations are to be satisfied by the same values of x and y
simultaneously. If such values of x and y exist, then they
are said to form a solution for the system of linear equations. In the three equations, x and
y appear in first degree only. Hence they are said to form a
system of linear equations in two unknowns x and y . They are
also called simultaneous linear equations
in two unknowns x and y .
The system has three linear equations in two unknowns x and y .
The equations represent three straight lines in two-dimensional
analytical geometry.
In this section, we develop methods using matrices to find
solutions of systems of linear equations.
Related Topics
Privacy Policy, Terms and Conditions, DMCA Policy and Compliant
Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.