Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

(i) Intersecting lines

(ii)Parallel lines

(iii)Coincident lines

Answer :

Ans.(i) Intersecting lines

The condition for intersecting lines is :

\({{a_1}\over {a_2}} \ne {{b_1}\over {b_2}}\)

So the second equation can be \(x + 2y = 3\)

Since, \({{a_1}\over {a_2}} \ne {{b_1}\over {b_2}}\)

=>\({{2}\over {1}} \ne {{3}\over {2}}\)

(ii) Parallel lines

The condition for parallel lines is :

\({{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}\)

So the second equation can be \(2x + 3y – 2 = 0 \)

Since, \({{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}\)

=>\({{2}\over {2}} = {{3}\over {3}} \ne {{-8}\over {-2}}\)

(ii) Coincident lines

The condition for coincident lines is :

\({{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}\)

So the second equation can be \(4x + 6y – 16 = 0 \)

Since, \({{a_1}\over {a_2}} = {{b_1}\over {b_2}} = {{c_1}\over {c_2}}\)

=>\({{2}\over {4}} = {{3}\over {6}} = {{-8}\over {-16}}\)

=>\({{1}\over {2}} = {{1}\over {2}} = {{1}\over {2}}\)

- 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.
- On comparing the ratios \({{a_1}\over {a_2}},{{b_1}\over {b_2}},{{c_1}\over {c_2}}\) find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (i) \(5x - 4y + 8 = 0, 7x + 6y – 9 = 0\) (ii)\(9x + 3y + 12 = 0, 18x + 6y + 24 = 0\) (iii)\( 6x - 3y + 10 = 0, 2x – y + 9 = 0\)
- Q3. 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)\(\frac{4}{3}x + 2y = 8, 2x + 3y = 12\)
- 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)\( 2x + y = 6, 4x - 2y = 4\)(iv)\(2x - 2y – 2 = 0, 4x - 4y – 5 = 0\)
- Half the perimeter of a rectangle garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
- 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.

- NCERT solutions for class 10 maths chapter 1 Real Numbers
- NCERT solutions for class 10 maths chapter 1 Electricity, Light , Carbon and it's compounds
- NCERT solutions for class 10 maths chapter 2 Polynomials
- NCERT solutions for class 10 maths chapter 3 Pair of linear equations in two variables
- NCERT solutions for class 10 maths chapter 4 Quadratic Equations
- NCERT solutions for class 10 maths chapter 5 Arithmetic Progressions
- NCERT solutions for class 10 maths chapter 6 Triangles
- NCERT solutions for class 10 maths chapter 7 Coordinate Geometry
- NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry
- NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry
- NCERT solutions for class 10 maths chapter 10 Circles
- NCERT solutions for class 10 maths chapter 11 Constructions
- NCERT solutions for class 10 maths chapter 12 Areas related to circles
- NCERT solutions for class 10 maths chapter 13 Surface Areas and Volumes
- NCERT solutions for class 10 maths chapter 14 Statistics
- NCERT solutions for class 10 maths chapter 15 Probability

- NCERT solutions for class 10 science chapter 1 Chemical Reactions and Equations
- NCERT solutions for class 10 science chapter 2 Acids, Bases and Salts
- NCERT solutions for class 10 science chapter 3 Metals and Non Metals
- NCERT solutions for class 10 science chapter 4 Carbon and its Compounds
- NCERT solutions for class 10 science chapter 5 Periodic Classification of Elements
- NCERT solutions for class 10 science chapter 6 Life Processes
- NCERT solutions for class 10 science chapter 7 Control and Coordination
- NCERT solutions for class 10 science chapter 8 How do Organisms Reproduce
- NCERT solutions for class 10 science chapter 9 Heredity and Evolution
- NCERT solutions for class 10 science chapter 10 Light Reflection and Refraction
- NCERT solutions for class 10 science chapter 11 Human Eye and Colorful World
- NCERT solutions for class 10 science chapter 12 Electricity
- NCERT solutions for class 10 science chapter 13 Magnetic Effect of Electric Current
- NCERT solutions for class 10 science chapter 14 Sources of Energy
- NCERT solutions for class 10 science chapter 15 Our Environment
- NCERT solutions for class 10 science chapter 16 Management of Natural Resources