# Systems of Equations

• Oct 6th 2008, 02:52 PM
~berserk
Systems of Equations
Given points(-2,-25),(1,-4),(3,-10) find the equation.

First i put the points into y=ax^2+bx=c form getting:
A: 4a-2b+c= -25
B: a+b+c= -4
C: 9a+3b+c= -10

then I solve for A:+B: and get D: 3a-3b= -21

then I go to solve for A:+C; and get E: -5a-5b= -15

then I try to solve D:+E: and get to 15a-15b= -105
.................................................-15a -15b= 75

what do i do if the a and b variables both cancel out?
• Oct 6th 2008, 02:57 PM
icemanfan
Well, in your case, a and b do not both cancel out when you add those two equations. If they did, either the two equations would be the same, or they would be different, in which case you would end up with a contradiction.
• Oct 6th 2008, 02:58 PM
~berserk
so where did i go wrong? Solving for A:+B: A:+C: or D:+E:
• Oct 6th 2008, 02:59 PM
icemanfan
You didn't. Simply add the two equations D and E, yielding -30b = -30.
• Oct 6th 2008, 03:02 PM
~berserk
o wow, I'm an idiot, i didn't see that the 15's were both negative, sorry for that, thanks though(Nod)
• Oct 6th 2008, 03:15 PM
jaydee323
Systems of Equations
Given points(-2,-25),(1,-4),(3,-10) find the equation.

First i put the points into y=ax^2+bx=c form getting:
A: 4a-2b+c= -25
B: a+b+c= -4
C: 9a+3b+c= -10

then I solve for A:+B: and get D: 3a-3b= -21

then I go to solve for A:+C; and get E: -5a-5b= -15

then I try to solve D:+E: and get to 15a-15b= -105
.................................................-15a -15b= 75

what do i do if the a and b variables both cancel out?

5 times D: 15a-15b= -105
3 times E:3.-15a -15b= 75

Note equation 3 times E should read -15a-15b= -45