1107 MrG How do we solve a Non Linear System?

2605 days ago by MATH4R2013

#1) find all POIs: 3*x-y==-2, 2*x^2-y==0 var('y') show(solve(3*x-y==-2,y)) show(solve(2*x^2-y==0,y)) 
       

solve([3*x-y==-2, 2*x^2-y==0],x,y) 
       
plot([3*x+2,2*x^2],-1,3) 
       
plot([3*x+2,2*x^2],-1,3,aspect_ratio=1) 
       
#2) Find all POIs: x^2+y^2==13, x^2-y==7 show(solve(x^2+y^2==13,y)) show(solve(x^2-y==7,y)) 
       

solve([x^2+y^2==13,x^2-y==7],x,y) 
       
plot([-sqrt(13-x^2),sqrt(13-x^2),x^2-7],-sqrt(13),sqrt(13),aspect_ratio=1) 
       
#3) Find all POIs: x^2-y^2==4, y==x^2 solve([x^2-y^2==4,y==x^2],x,y) 
       
show(solve(x^2-y^2==4,y)) 
       
a=plot([-sqrt(x^2-4)],-4,-2,color='red') b=plot([-sqrt(x^2-4)],2,4,color='red') c=plot([sqrt(x^2-4)],-4,-2,color='green') d=plot([sqrt(x^2-4)],2,4,color='green') e=plot([x^2],-4,4,color='orange') show(a+b+c+d+e,aspect_ratio=1)