**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) 5*x* – 4*y* + 8 = 0

7*x* + 6*y* – 9 = 0

(ii) 9*x* + 3*y* + 12 = 0

18*x* + 6*y* + 24 = 0

(iii) 6*x* – 3*y* + 10 = 0

2*x* – *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) 3*x* + 2*y* = 5

2*x* – 3*y* = 7

(ii) 2*x* – 3*y* = 8 ; 4*x* – 6*y* = 9

(iii) { \displaystyle \frac{3}{2}x + \frac{5}{3}y = 7; 9x-10y=14}

(iv) 5*x* – 3*y* = 11 ; – 10*x* + 6*y* = –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, 2*x* + 2*y* = 10

(ii) *x* – *y* = 8, 3*x* – 3*y* = 16

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

(iv) 2*x* – 2*y* – 2 = 0, 4*x* – 4*y* – 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