Question

Form the pair of linear equations in the following problems, and find their solution graphically:

(i) 10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
 

(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

(iii) 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.

Answer 1

(i) Let the number of girls and boys in the class be x and y respectively. According to the given conditions, we have:

Three solutions of this equation can be written in a table as follows:

Three solutions of this equation can be written in a table as follows:

From the graph, it can be observed that the two lines intersect each other at the point (7,3) .so x=7 and y=3

Thus, the number of girls and boys in the class are 7 and 3 respectively.
(ii) Let the cost of one pencil and one pen be Rs x and Rs y respectively. According to the given conditions, we have:

Three solutions of this equation can be written in a table as follows:

Three solutions of this equation can be written in a table as follows:

From the graph. It can be observed that the two lines intersect each other at the point (3,5). so. x=3 and y=5

Therefore, the cost of one pencil and one pen are Rs 3 and Rs 5 respectively

(iii) Let us denote the number of pants by x and the number of skirts by y. Then the equations formed are:

Plot the point and draw the lines passing through them to represent the equation, as shown in fig.

The t lines intersect at the point (10) . so. x-1, y=0 is the required solution of the pair of linear equations, i.e, the number of pants she purchased island she did not buy any skirt Concept insight: Read the question carefully and examine what are the unknowns. Represent the given conditions with the help of equations by taking the unknowns quantities as variables. Also carefully state the variables as whole solution is based on it on the graph paper, mark the points accurately and neatly using a sharp pencil. Also take at least three points satisfying the two equations in order to obtain the correct straight line of the equation. Since joining any two points gives a straight line and if one of the points is computed incorrect will give a wrong line and taking third point will give a correct line. The point where the two straight lines will intersect will give the values of the two variables, i.e., the solution of the two linear equations. State the solution point