Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
DifficultForm the pair of linear equations in the following problems,and find their solutions graphically.
$10$ 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.
$10$ 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.
(N/A) Let the number of girls be $x$ and the number of boys be $y$.
According to the question,the algebraic representation is:
$x + y = 10$
$x - y = 4$
For $x + y = 10$,we have $x = 10 - y$:
For $x - y = 4$,we have $x = 4 + y$:
By plotting these points on a graph,we observe that the lines intersect at the point $(7, 3)$.
Therefore,the number of girls is $7$ and the number of boys is $3$.
According to the question,the algebraic representation is:
$x + y = 10$
$x - y = 4$
For $x + y = 10$,we have $x = 10 - y$:
| $x$ | $5$ | $4$ | $6$ |
| $y$ | $5$ | $6$ | $4$ |
For $x - y = 4$,we have $x = 4 + y$:
| $x$ | $5$ | $4$ | $3$ |
| $y$ | $1$ | $0$ | $-1$ |
By plotting these points on a graph,we observe that the lines intersect at the point $(7, 3)$.
Therefore,the number of girls is $7$ and the number of boys is $3$.
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