SOLVING LINEAR EQUATIONS IN TWO VARIABLES USING GRAPHICAL METHOD

Solving Linear Equations in Two Variables Using Graphical Method :

In this section, we will learn, how to solve linear equations in two variables using graphical method.

Solving Linear Equations in Two Variables Using Graphical Method Examples

Example 1 :

Form the pair of linear equations in the following problems, and find their solutions graphically.

(i) 10 students of class X took part in a 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.

Solution :

Total number of students in the class = 10

Let “x” be the number of boys

Let “y” be the number of girls

Number of girls is 4 more than the number of boys

y = x + 4

x – y = - 4 -----(1)

Total number of boys + number of girls = 10

x + y = 10  -----(2)

y = 10 – x

So far we have formed two equations from the above given information. Now we need to make a graph.

The above lines are intersecting at the point (3, 7).

So, the number of boys  =  3 and number of girls  =  7

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

Solution :

Let “x” be the cost of one pencil

Let “y” be the cost of one pen

5 x + 7 y = 50 -------(1)

7 x + 5 y = 46 -------(2)

They are intersecting at the point (3, 5).

So, the cost of one pencil = 3 and cost of one pen = 5

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