Question

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?

Answer 1

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

Answer 2

I understand how to do that, thats substitution. How can I solve it with elimination?

Answer 3

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

Answer 4

Sorry :) I must've gotten something confused. I think I get it now. Thank you!

Answer 5

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?

Answer 6

*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)