Question

On comparing the ratios a1a2, b1b2, and c1c2, 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​

Answer 1

$\huge\underline\mathrm{Question}:-$

On comparing the ratios a1a2, b1b2, and c1c2, 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

$\huge\underline\mathrm{Solution}:-$

(i) Given : 3x + 2y = 5 or 3x + 2y -5 = 0

Given : 3x + 2y = 5 or 3x + 2y -5 = 0and 2x – 3y = 7 or 2x – 3y -7 = 0

Comparing these equations with a1x + b1y + c1=0

And a2x + b2y + c2 = 0

We get,

a1=3, b1= 2, c1= -5

a2=2, b2=-3, c2=-7

a1/a2 = 3/2, b1/b2 = 2/-3, c1/c2 = -5/-7 = 57

Since, a1/a2≠b1/b2

So, the given equations intersect each other at one point and they have only one possible solution. The equations are consistent.

(ii) Given 2x – 3y = 8 and 4x – 6y = 9

Therefore,

a1=2, b1= -3, c1= -8

a2=4, b2=-6, c2=-9

a1/a2=2/4=1/2, b1/b2=3/6=1/2, c1/c2=8/9

Since, a1/a2=b1/b2≠c1/c2

So, the equations are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.

Answer 2

Answer:

heloo mate ❤

Step-by-step explanation:

:−

On comparing the ratios a1a2, b1b2, and c1c2, 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

\huge\underline\mathrm{Solution}:-

Solution

:−

(i) Given : 3x + 2y = 5 or 3x + 2y -5 = 0

Given : 3x + 2y = 5 or 3x + 2y -5 = 0and 2x – 3y = 7 or 2x – 3y -7 = 0

Comparing these equations with a1x + b1y + c1=0

And a2x + b2y + c2 = 0

We get,

a1=3, b1= 2, c1= -5

a2=2, b2=-3, c2=-7

a1/a2 = 3/2, b1/b2 = 2/-3, c1/c2 = -5/-7 = 57

Since, a1/a2≠b1/b2

So, the given equations intersect each other at one point and they have only one possible solution. The equations are consistent.

(ii) Given 2x – 3y = 8 and 4x – 6y = 9

Therefore,

a1=2, b1= -3, c1= -8

a2=4, b2=-6, c2=-9

a1/a2=2/4=1/2, b1/b2=3/6=1/2, c1/c2=8/9

Since, a1/a2=b1/b2≠c1/c2

So, the equations are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.❤❤