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Linear Equations in Two Variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsLinear Equations in Two Variables5 Marks
Question
Form the pair of linear equations in the following problems, and find their solution graphically:
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.
✓

Answer

Let the number of girls and boys in the class be x and y respectively.
According to the given conditions, we have,
x + y = 10
x - y = 4
x + y = 10
⇒ x = 10 - y
Three solutions of this equations can be written in a table as follows,
x
4
5
6
y
6
5
4
x - y = 4
⇒ x = 4 + y
Three solutions of this equation can be written in a table as follows.
x
5
4
3
y
1
0
-1
The graphical representation is as follows.

From the graph, it can be observes 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.

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