SOLUTION: Find the value/s of 'a' such that the following simultaneous equations have infinitely many solutions. ax+3y=0 2x+(a+1)y=0 I got 2 and -3 for the value of a, am i correct?

Question 1021827: Find the value/s of 'a' such that the following simultaneous equations have infinitely many solutions.
ax+3y=0
2x+(a+1)y=0
I got 2 and -3 for the value of a, am i correct?
Found 2 solutions by robertb, Fombitz:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
For a (square) homogeneous system of linear equations to have non-trivial solutions, the determinant of coefficients

==>, or ==> (a+3)(a-2) = 0
==> a = -3 or 2.
So your answers are correct.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For infinitely many solutions, the equations are multiples of each other.
(a,3)*n=(2,a+1)
1.
2.
Substituting 1 into 2,

Then,

and

Yes, correct.

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