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.
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.
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.
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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