Question

On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2) find out whether the following pair of linear equations are consistent, or inconsistent. (i) 3x + 2y = 5 ; 2x – 3y = 7

Answer 1

Answer:

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

and 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 = 5/7

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.

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Answer 2

Answer:

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