S.O.S. Mathematics CyberBoard

[vnayudu]

Question : For what values of 'a' and 'b' , the simultaneous equations
x + y + z = 6
x + 2y + 3z = 10
x + 2y + az = b

have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solution

[math4ever]

What have you tried?
Try subtracting the second equation from the third equation (subtract left sides, then right sides). This will eliminate x and y. Solve the resulting equation for z.
You will get z in terms of a and b ( a fraction).
From that expression you can easily answer the 3 questions.
No solution --> denominator = 0 and numerator is not 0.
Infinitely many sol --> den = 0 and num = 0
One sol --> what do you think?
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