Expert: Abe Mantell - 7/7/2009

Question
1) If x(2x+1)=0 and (x+1/2)(2x-3)=0, then x=?

2) For what values of 'k' will the pair of equations 3x+4y=12 and kx+12y=30 not have a unique solution?


Answer
1) x(2x+1)=0 gives x=0 or x=-1/2, (x+1/2)(2x+3)=0 gives x=-1/2 or x=-3/2
.. so the only value in common is x=-1/2

2) When the lines are parallel and not intersecting there will be no
.. no solution.  We see that 12y is 3 times the 4y in the first equation.
.. So we need kx to be 3 times the 3x, so k=3*3=9...this makes the lines
.. parallel, and since 30 is not 3 times 12 (meaning they are not the
.. same lines with infinitely many solutions), there will be no solution.

I hope this helps!

Abe