SOLUTION: How would you find the points that the graphs of the equation in the following systems have in common? x^2+y^2=4 x=y

Question 89877: How would you find the points that the graphs of the equation in the following systems have in common?
x^2+y^2=4
x=y
Found 2 solutions by jim_thompson5910, checkley75:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Plug in y=x

Combine like terms

Divide both sides by 2

Take the square root of both sides

So our solutions are (,) and (,)

Check:

works

or

works

We can also verify with this graph

and if you used Pythagoreans theorem, you would verify your answer.

Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
FIRST I WOULD PLOT THEM & SEE IF THERE IS ANY OBVIOUS SOLUTION.
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = x and y^2 = -x^2
+4).
OR SET X=Y & SOLE FOR Y IN THE FIRST EQUATION
Y^2+Y^2=4
2Y^2=4
Y^2=4/2
Y^2=2
Y=+/-1.414 ANSWER.
X=Y=+/-1.414 ANSWER.
RELATED QUESTIONS
Given the quadratic function y=x^2-x+k-1 and the linear function y=x+1, find the number... (answered by robertb)
I can figure out how to do the graphs. I just don't know how to figure out the plotting... (answered by lotanez)
Find the points of intersection, if any, of the graphs in the system y^2+4x=0... (answered by htmentor)
In how many points do the graphs of 2(x+1)^2 + (y-2)^2 = 25 and 4(x+1)^2 +3(y-2)^2= 15... (answered by greenestamps)
How do we find the points for the equation y=(1.2)^(-x)sinx I mean can you please tell... (answered by Fombitz)
If the difference of the roots of the equation 2x2 − (a +1)x+a−1 = 0 is equal (answered by ikleyn)
3) For the equation x - 2 sqrt x = 0, perform the following: a) Solve for all values of... (answered by rapaljer)
5) For the equation x-2√x=0 , perform the following: a) Solve for all values of... (answered by venugopalramana)
For the equation x-2^x=0 , perform the following: a) Solve for all values of x that... (answered by rapaljer)