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# 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.

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 â‚ą 440. Person B purchases 6 Kilograms of rice and 2 Kilograms of sugar and pays â‚ą 400. Person C purchases 8 Kilograms of rice and 5 Kilograms of sugar and pays â‚ą 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 â‚ą 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 .

### 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.

Tags : Applications of Matrices: Solving System of Linear Equations , 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants
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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Formation of a System of Linear Equations | Applications of Matrices: Solving System of Linear Equations