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
Solution
(i) 3x
+ 2y = 5 ; 2x – 3y = 7
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
(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
No comments:
Post a Comment