Topics Covered
Graphical and Algebraical Tests for Parallel lines, intersecting lines and coincident lines
NCERT Exercise 3.2 Question 2 On comparing the ratios { \displaystyle \frac{a_1}{a_2}, \frac{b_1}{b_2}} and { \displaystyle \frac{c_1}{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
Consistent and Inconsistent pair of linear equations in two variables (unique solution, no solution, infinite solution)
NCERT Exercise 3.2 Question 3 On comparing the ratios { \displaystyle \frac{a_1}{a_2}, \frac{b_1}{b_2}} and { \displaystyle \frac{c_1}{c_2}} find out whether the lines representing the
following pairs of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5
2x – 3y = 7
(ii) 2x – 3y = 8 ; 4x – 6y = 9
(iii) { \displaystyle \frac{3}{2}x + \frac{5}{3}y = 7; 9x-10y=14}
(iv) 5x – 3y = 11 ; – 10x + 6y = –22
(v) { \displaystyle \frac{4}{3}x + 2y = 8; 2x+3y=12}
NCERT Exercise 3.2 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
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
NCERT Exercise 3.2 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.
NCERT Exercise 3.2 Question 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