Question

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

Answer 1

Answer:

it is a unique solution and consistent

Step-by-step explanation:

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Answer 2

REQUIRED ANSWER : -

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

and 2x – 3y = 7 or 2x – 3y – 7 = 0

Comparing the above equations with a1x + b1y + c1=0

And a2x + b2y + c2 = 0

We get,

$\longrightarrow$ a1 = 3, b1 = 2, c1 = -5

$\longrightarrow$ a2 = 2, b2 = -3, c2 = -7

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

➠ Since, a1/a2≠b1/b2 the lines intersect each other at a point and have only one possible solution.

Hence, the equations are consistent.

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

Therefore,

$\longrightarrow$ a1 = 2, b1 = -3, c1 = -8

$\longrightarrow$ a2 = 4, b2 = -6, c2 = -9

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

Since, a1/a2=b1/b2≠c1/c2

Hence, the equations are inconsistent.