Exercise 3.1
Question 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.
Solution :
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Question 1: (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.
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Question 2: On comparing the ratios a1/a2 , b1/b2 & c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) 5x – 4y + 8 = 0 (ii) 9x + 3y + 12 = 0 (iii) 6x – 3y + 10 = 0
7x + 6y – 9 = 0 18x + 6y + 24 = 0 2x – y + 9 = 0
Solution :
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Question 3 : On comparing the ratios a1/a2, b1/b2 & c1/c2 , find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5 ; 2x – 3y = 7 (ii) 2x – 3y = 8 ; 4x – 6y = 9
(iii) 3x/2 + 5y/3= 7 ; 9x – 10y = 14 (iv) 5x – 3y = 11 ; – 10x + 6y = –22
(v) 4x/3 + 2y= 8 ;2x + 3y = 12
Solution :
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Question 4: Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
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Question 4 : (iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
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Question 5: 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.
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Question 6 : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variable ssuch that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines
(iii) coincident lines
Solution:
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Question 7: Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Solution :
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