Does anybody know how I can use these two equations x^2 =-y and x=-y^2 to find the points (0,0) and (-1,-1)?
these are what I have done
I plug equation1 into equation2-->x=(x^2)^2-->x=x^4-->0=x^4 -x--> 0=x(x^3 -1)-->x=0 and1
Now I plug those points into equation1--> (0)^2 =-y-->0=y so point1= (0,0), (1)^2 =-y-->y=-1 so point2=(1,-1) What did I do wrong?
well, (0,0) is clearly a solution
x = -y^2, so
x^2 = (-y^2)^2 = y^4 = -y
y^3 = -1
y = -1
So, x = -(-1)^2 = -(-1) = 1
so (1,-1) also a solution
check that 2nd last line:
So, x = -(-1)^2 = -(-1) = 1
so (1,-1) also a solution
should be:
So, x = -(-1)^2 = -(+1) = -1
so (-1,-1) also a solution
@ anonymous
Why are you repeating this question when it was answered yesterday,
and you even acknowledged that you got it.
This just makes tutors doing unnecessary work.
https://www.jiskha.com/questions/1828146/can-somebody-explains-what-i-did-wrong-find-the-points-0-0-and-1-1-eq1-x-2-y
Btw, give yourself a nickname, it makes things so much easier.
I have a lot to do so when I go from one subject to another, I forgot what I have done the day before sometime even hours before. Poor memory or too much stress. I told my teacher that I can not learn just by doing homework. I need time to review or I learn nothing but his way of learning is by doing lot of homework and assignment, which is worst for me.
If you'd give yourself a nickname, as Reiny suggested, that would help. Then you could use Ctrl+F to find your previous posts.
In addition, if you bookmark each question you post (Ctrl+D on a PC), you'll easily be able to find what you've already posted and check back to find the tutors' replies.
In your solution process, you made a mistake when you concluded that x=0 and x=1. Let's go through the steps again and see where the error occurred.
Starting with the equations x^2 = -y and x = -y^2:
1. Substitute the value of x from equation 2 into equation 1:
(-y)^2 = -y
y^2 = -y
2. Now, rearrange the equation to bring all terms to one side:
y^2 + y = 0
3. Factor out the common term y:
y(y + 1) = 0
At this point, you correctly identified two possible solutions: y = 0 and y = -1. To find the corresponding x-values for these points, substitute the values of y back into either equation:
For y = 0:
x = -(0^2) = 0
So the first point is (0, 0).
For y = -1:
x = -(-1^2) = -1
So the second point is (-1, -1).
To summarize, the correct points are (0, 0) and (-1, -1), which you found correctly in your solution. It seems that you just made an error in identifying the possible solutions for x earlier.