1.4.1 Formation of a System of Linear Equations

. . 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 Kilograms of rice and Kilograms of sugar and pays ` . Person B purchases Kilograms of rice and Kilograms of sugar and pays ` . Person C purchases Kilograms of rice and Kilograms of sugar and pays ` . 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 Kilograms of rice and Kilograms sugar and pays ` . So, . Similarly, by considering Person B and Person C, we get .

Hence the mathematical model is to obtain x and y such that , , Note 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.