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‚¹ 440. Person B purchases
6 Kilograms of rice and 2 Kilograms of sugar and pays â‚¹ 400.
Person C purchases 8 Kilograms of rice and 5 Kilograms of sugar and pays â‚¹ 720.
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‚¹ 440 . So, 5*x *+ 3*y *= 440 . Similarly, by considering Person B and Person C, we get 6*x
*+ 2 *y *= 400 and 8*x *+ 5 *y *= 720 . Hence the
mathematical model is to obtain *x *and *y *such that

5*x *+ 3*y *= 440, 6*x *+ 2 *y *= 400, 8*x *+ 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.

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

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