consistent. Example : Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: x – y + = x – y + = Solution : Multiplying Equation ( ) by , we get x – y + = But, this is the same as Equation ( ). Hence the lines represented by Equations ( ) and ( ) are coincident. Therefore, Equations ( ) and ( ) have infinitely many solutions.
Plot few points on the graph and verify it yourself. Example : Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”.
Help her friends to find how many pants and skirts Champa bought. Solution : Let us denote the number of pants by x and the number of skirts by y. Then the equations formed are : y = x – y = x – Let us draw the graphs of Equations ( ) and ( ) by finding two solutions for each of the equations. They are given in Table .
. Table . y = x – – y = x – – Plot the points and draw the lines passing through them to represent the equations, as shown in Fig. .
. The two lines intersect at the point ( , ). So, x = , y = is the required solution of the pair of linear equations, i.e., the number of pants she purchased is and she did not buy any skirt. Verify the answer by checking whether it satisfies the conditions of the given problem.
EXERCISE . . Form the pair of linear equations in the following problems, and find their solutions graphically. (i) students of Class X took part