Ncert Solutions for Class 10 Maths

Exercise 3.2 (Graphical Method of Solution of a Pair of Linear Equations)

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. (ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

2. On comparing the ratios \(a_1 \over a_2\),\(b_1 \over b_2\) and \(c_1 \over c_2\), 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 and 7x+ 6y– 9 = 0 (ii) 9x+ 3y+ 12 = 0 and 18x+ 6y+ 24 = 0 (iii) 6x– 3y+ 10 = 0 and 2x– y+ 9 = 0

3. On comparing the ratios \(a_1 \over a_2\),\(b_1 \over b_2\) and \(c_1 \over c_2\), 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) \({3\over 2}x + {5 \over 3} y = 7\) ; 9x– 10y = 14 (iv) 5x– 3y = 11 ; –10x+ 6y = –22 (v) \({4 \over 3}x + 2y = 8\) ; 2x+ 3y = 12

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 (iii) 2x+ y– 6 = 0, 4x– 2y– 4 = 0 (iv) 2x– 2y– 2 = 0, 4x– 4y– 5 = 0

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.

6. Given the linear equation 2x+ 3y– 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is : (i) intersecting lines (ii) parallel lines (iii) coincident lines

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.

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