x^2 = x + 2
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x - 2 = 0 ... x = 2
x + 1 = 0 ... x = -1
the line intersects the parabola in two places
plug the x-values into the equations to find the corresponding y-values
I have to solve a few systems through elimination, but I'm still not quite sure how to do it..
The first is y=x^2 and y=x+2
Can someone show me how exactly it is worked out so I can try the second one myself?
6 answers
I understand how to do that, thats substitution. How can I solve it with elimination?
if you subtract the equations (to eliminate y), you still end up with
... 0 = x^2 - x - 2
... but you have used elimination
even with elimination, you have to substitute back at some point to find all the variables
... 0 = x^2 - x - 2
... but you have used elimination
even with elimination, you have to substitute back at some point to find all the variables
Sorry :) I must've gotten something confused. I think I get it now. Thank you!
Ok.. I understand how to eliminate y and everything, then you factor it as normal. The solutions to that equation were (-1, 1) and (2,4).
I'm working on another one and used the same steps.
y=48x+20
-(y=-x^2+200x+20)
and i ended up with :
0=x^2-152x
This can't be factored, does that mean it has no solution?
I'm working on another one and used the same steps.
y=48x+20
-(y=-x^2+200x+20)
and i ended up with :
0=x^2-152x
This can't be factored, does that mean it has no solution?
*facepalm* That tricked me. I think it's (152, 7316) & (0,20)? I guess ANY number times 0 is a factor of 0... So I did -152 x 0=0 and -152+0 = -152.
That gave me (x-152)(x+0)
That gave me (x-152)(x+0)
1 answer