maths assignment.pptx

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1. BY:S.LINGESHWAR MATH ASSIGNMENT

2. Introduction A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and two variables.  An equation of the form ax +by + c = 0 where a , b , and c are real numbers ,such that a and b are not both zero, is called a linear equation in two variables . A linear equation in two variable has infinitely many solution.  The graph of every linear equation in two variables is a straight line.

3. CONTINUED X=0 is the equation of the y-axis and y=0 is the equation of x-axis . The graph of x=0 is a straight line parallel to y-axis. The graph of y=0 is a straight line parallel to the x-axis . An equation of the type y=mx represents a line passing through the origin.  Every point on the graph of a linear equation in two variables is a solution of the linear equation .

4. How its obtain? The solutions of a linear equation can be obtained by substituting different values for x in the equation to find the corresponding values of y . The values of x and y are represented as an order pair. To plot the graph of a linear equation, its solutions are found algebraically and then the points are plotted on the graph . Any linear equation of the form 'ax + by + c = 0' represents a straight line on the graph. The points of the straight line make up the collection of solutions of the equation.

5. Algorithm Obtain the linear equation . Let the equation the equation be ax + by + c=0.  Give any three values to x and calculate the corresponding values of y to obtain solutions If possible ,choose integral values of x in such a way that the corresponding values of y are also integers.

6. Linear Equation in real life One of the realities of life is how so much of the world runs by mathematical rules. As one of the tools of mathematics, linear systems have multiple uses in the real world. Life is full of situations when the output of a system doubles if the input doubles, and the output cuts in half if the input does the same. That's what a linear system is, and any linear system can be described with a linear equation.

7. EXAMPLE ONE 4 chairs and 3 tables cost 2100 and 5 chairs and 2 tables cost 1750. Find the cost of a chair and a table separately . SOLUTION Let a chair be x and that of a table be y . Then,and , 4x + 3y = 2100, 5x + 2y = 1750 This system of equations, a1/a2≠b1/b2 ​ So,hence has a unique solution , dependent and   consistent

8. EXAMPLE 2 30 pens and 50 pencils together cost 100 , while 60 pens and 100 pencils together cost 200. Find the cost of a pen and that of a pencil . SOLUTION Let the cost of a pen be x and that of a pencil be y . Then , 30x + 50y = 100, 60x + 100y = 200 This system of equations: a1/a2=b1/b2=c1/c2 ;Has infinitly many solutions,dependent and consistant

9. EXAMPLE 3 35 fans and 25 tube lights together cost 15000, while 70 fans and 50 tube lights together cost 29000. Find the cost of a pen and that of a pencil . SOLUTION Let the cost of a fan be x and that of a tube light be y . Then , 35x + 25y = 15000, 70x + 5 0y = 29000 This system of equations: a1/a2=b1/b2 c1/c2 ;Has no solution ,independent and inconsistant