SOLUTION: X squared + y squared = 4 Y minus X = 1 We have to solve the system it says... But my teacher says that all we have to solve for is X and Y because it's a longer problem.

Question 1031015: X squared + y squared = 4
Y minus X = 1
We have to solve the system it says... But my teacher says that all we have to solve for is X and Y because it's a longer problem.

Found 2 solutions by Alan3354, fractalier:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
X^2 + y^2 = 4
Y - X = 1 --> y = x + 1
-----------
X^2 + y^2 = 4
Sub for y
x^2 + (x+1)^2 = 4
2x^2 + 2x + 1 = 4
2x^2 + 2x - 3 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=28 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.822875655532295, -1.8228756555323. Here's your graph:

=================
x = -1/2 - sqrt(7)/2
y = +1/2 - sqrt(7)/2
======================
x = -1/2 + sqrt(7)/2
y = +1/2 + sqrt(7)/2
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Yes, from
and
we solve the second one and substitute into the first one...we get
y = x + 1 and then
x^2 + (x+1)^2 = 4
x^2 + x^2 + 2x + 1 = 4
2x^2 + 2x - 3 = 0
This cannot be factored so we use the quadratic formula...
x = (-2 + sqrt(4 + 24))/4 = (-2 + sqrt(28))/4 = (-1 + sqrt(7))/2
and
x = (-2 - sqrt(4 + 24))/4 = (-2 - sqrt(28))/4 = (-1 - sqrt(7))/2
Plug in and solve for y, as in y = x + 1...
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