Question 3. On Comparing the Ratios A1/a2 , B1/b2  and C1/c2 Find Exercise 3.2 Chapter 3 Pair of Linear Equations in

Question 3. On comparing the ratios a1/a2 , b1/b2  and c1/c2 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) 3/2x + 5/3 y = 7 ; 9x – 10y = 14
(iv) 5x – 3y = 11 ; – 10x + 6y = –22
(v)4/3x + 2y =8  ; 2x + 3y = 12
(i) 3x + 2y = 5 ; 2x – 3y = 7
Solution: Convert the equation in form of  a₁x + b₁y + c₁ = 0  and a₂x+ b₂y + c₂ = 0
We get
3x + 2y - 5 =0  and  2x – 3y – 7  =0
Compare the equation with

We get
a1 = 3,            b1       = 2,                 and c1 = -5
a2 =2              b2        =-3                  and c2 = -7

We get

Hence both lines are Consistent
(ii) 2x – 3y = 8 ; 4x – 6y = 9
Convert the equation in form of  a₁x + b₁y + c₁ = 0  and a₂x+ b₂y + c₂ = 0
We get
2 x – 3 y - 8 = 0  and  4x – 6 y – 9  =0
Compare the equation with

We get
a1 = 2,            b1       = -3,               and c1 = - 8
a2 = 4             b2        = - 6                and c2 = - 9

So we get

So both lines are Inconsistent
(iii)        3/2x + 5/3 y = 7 ; 9x – 10y = 14
Convert the equation in form of a₁x + b₁y + c₁ = 0  and a₂x+ b₂y + c₂ = 0
We get
3/2 x  + 5/3 y - 7 = 0  and  9x – 10 y - 14  =0
Compare the equation with

We get
a1 = 3/2,         b1       = 5/3,             and c1 = - 7
a2 = 9             b2        = - 10              and c2 = - 14

So we get

So both lines are Consistent
(iv)        5x – 3y = 11 ; – 10x + 6y = –22
Convert the equation in form of a₁x + b₁y + c₁ = 0  and a₂x+ b₂y + c₂ = 0
We get
5 x  -3 y - 11 = 0  and  -10 x + 6 y + 22 =0
Compare the equation with

We get
a1 = 5             b1        = - 3,              and c1 = - 11
a2 = -10          b2        =  6                  and c2 =   22

So we get

Hence
So both lines are dependent and consistent  
(v)4/3x + 2y =8  ; 2x + 3y = 12
Convert the equation in form of a₁x + b₁y + c₁ = 0  and a₂x+ b₂y + c₂ = 0
We get
4/3 x  + 2 y - 8 = 0  and  2x + 3 y - 12  =0
Compare the equation with

We get
a1 = 4/3,         b1       = 2,                 and c1 = -8
a2 = 2             b2        = 3                   and c2 = - 12

So we get

So both lines are Dependent and consistent