1. ## 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?

2. 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.

3. so where did i go wrong? Solving for A:+B: A:+C: or D:+E:

4. You didn't. Simply add the two equations D and E, yielding -30b = -30.

5. o wow, I'm an idiot, i didn't see that the 15's were both negative, sorry for that, thanks though

6. 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