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Linear Equations in Two Variables — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsLinear Equations in Two Variables4 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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