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Pair Of Linear Equations In Two Variables
(i) 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.
(i) Let the number of boys be x and number of girls be y.
Case I. x + y = 10 ...(i)
Case II. y = x + 4
⇒ x - y = -4 ...(ii)
We have, x + y = 10
⇒ x = 10 - y
Thus, we have following table :
Fig. 3.4.
We have, x - y = -4
⇒ x = y - 4
Thus we have following table :
When we plot the graph of the given equation, we find that both the lines intersect at me point (3, 7). So.r = 3,y = 7 is the required solution of the pair of linear equation.
Hence, the number of boys be 3 and the number of girls be 7, who took part in quiz.
Some More Questions From Pair of Linear Equations in Two Variables Chapter
Which of the following pairs of linear equations are consistent/inconsistent ? Consistent, obtain the solution graphically :
2x + y – 6 = 0, 4x – 2y – 4 = 0
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Given the linear equations 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representing of the pair so formed is :
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines.
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