The Student
Junior Member
- Joined
- Apr 25, 2012
- Messages
- 241
The question wants me to find the intersection/s for y = 2x and x^2 + y^2 = 1.
I know that this is just a line going through a circle, but a problem arises when I actually work out the solution set.
So I start by substituting 2x with the y in x^2 + y^2 = 1. That gives x^2 + 4x^2 = 1. Then isolating x I get x = +/-(1/5)^(1/2).
Now I will plug in the negative value for x in x^2 + y^2 = 1. (-(1/5)^(1/2))^2 + y^2 = 1. Then y^2 = 4/5. Finally y = +/-(4/5)^(1/2)
But on the graph, we know that one of the solution set cannot be ( -(1/5)^(1/2), (4/5)^(1/2) ) .
I get the correct solution set when I plug the values that I found for x into y = 2x.
Why do the solutions that I found for x work in y = 2x but not in x^2 + y^2 = 1?
I know that this is just a line going through a circle, but a problem arises when I actually work out the solution set.
So I start by substituting 2x with the y in x^2 + y^2 = 1. That gives x^2 + 4x^2 = 1. Then isolating x I get x = +/-(1/5)^(1/2).
Now I will plug in the negative value for x in x^2 + y^2 = 1. (-(1/5)^(1/2))^2 + y^2 = 1. Then y^2 = 4/5. Finally y = +/-(4/5)^(1/2)
But on the graph, we know that one of the solution set cannot be ( -(1/5)^(1/2), (4/5)^(1/2) ) .
I get the correct solution set when I plug the values that I found for x into y = 2x.
Why do the solutions that I found for x work in y = 2x but not in x^2 + y^2 = 1?
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