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1. Real Numbers
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
2. Polynomials
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise 2.4
3. Pair of Linear Equations in Two Variables
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Exercise 3.5
Exercise 3.6
Exercise 3.7
4. Quadratic Equations
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
5. Arithmetic Progressions
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
6. Triangles
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise 6.4
Exercise 6.5
Exercise 6.6
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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Graphical Method of Solution of a Pair of Linear Equations (Video) [Full Exercise 3.2]
Ncert Solution for Class 10 (Mathematics)
Important Class 10 Links
1. Real Numbers
2. Polynomials
3. Pair of Linear Equations in Two Variables
4. Quadratic Equations
5. Arithmetic Progressions
6. Triangles