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Under what conditions on a and b will the following linear system have no solutions, one solution, infinitely many solu- tions?2x − 3y = a4x − 6y = b

Question

Under what conditions on a and b will the following linear system have no solutions, one solution, infinitely many solu- tions?

2x − 3y = a

4x − 6y = b

 

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Step 1

The given linear equations are,

2x – 3y = a and 4...

Equate the equations to the lines ar by+c =0 and azx+b,y+c, = 0 respectively
-
Then,
a 2, b3 and e, =-a
1
a24, b6 and c, =-b
Condition for the system has no solution if
#
C2
The system has exactly one solution if
The system has infinitely many solutions if "1= 1-1
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Equate the equations to the lines ar by+c =0 and azx+b,y+c, = 0 respectively - Then, a 2, b3 and e, =-a 1 a24, b6 and c, =-b Condition for the system has no solution if # C2 The system has exactly one solution if The system has infinitely many solutions if "1= 1-1

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