AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Organizations belong to NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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.
