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?

Algebra ->  Coordinate Systems and Linear Equations -> 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?      Log On


   

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) About Me  (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
det%28matrix%28+2%2C+2%2C+%0D%0A+++a%2C+3%2C%0D%0A+++2%2C+a%2B1%0D%0A+%29%29+=+0
==>a%28a%2B1%29+-+6+=+0, or a%5E2+%2B+a+-+6+=+0 ==> (a+3)(a-2) = 0
==> a = -3 or 2.
So your answers are correct.

Answer by Fombitz(32388) About Me  (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.a%2An=2
2.3%2An=a%2B1
Substituting 1 into 2,
3%282%2Fa%29=a%2B1
6%2Fa=a%2B1
6=a%5E2%2Ba
a%5E2%2Ba-6=0
%28a%2B3%29%28a-2%29=0
Then,
a%2B3=0
a=-3
and
a-2=0
a=2
Yes, correct.