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Question

On comparing the ratiosa1a2,b1b2,c1c2, find out whether the following pairs of linear equations are consistent or inconsistent:

3x+2y=52x-3y=7


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Solution

Step 1: Analyzing the condition by which lines are intersecting, parallel or coincident :

If we are given a set of two linear equations,

a1x+b1y+c1=0

a2x+b2y+c2=0 , then

  • lines are consistent, if a1a2b1b2 and a1a2=b1b2=c1c2
  • lines are inconsistent if a1a2=b1b2c1c2

Step 2: Verify the given set of the equations:

The equations are -

3x+2y=52x-3y=7

By comparing the given equations with

a1x+b1y+c1=0

a2x+b2y+c2=0,

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

a1a2=32,b1b2=2-3c1c2=57

Since, a1a2b1b2, therefore the given equations intersect each other at one point and they have only one possible solution.

Hence, the given set of linear equations are consistent.


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