#x and y are variables
y= var('y')
#x=3
#y=2

#denote A
#area of a square
A(x,y)= (x*y+y**2+x**2+x*y)
print('A=',A)

#denote B
B(x,y)=((x+y)**2)
print('B=',B)

#evaluate the equations
x=3
y=2
print('With variables defined, A=',A(3,2))
print('With variables defined, B=',B(3,2))
# equation A and B are equal


#denote F
F(x)= (x*x+x**2+x**2+x*x)
print('F=', F)
#plot the function of f
p1=plot(F,-100,100, ymin=-2,ymax=100,gridlines='major')
p1.show()
#the area maximum is infinite
print('the area maximum is infinite')

#denote Q
Q=(8-x**2)
print('Q=',Q)
#plot the function Q
p2=plot(Q, -5,5, ymin=-5,ymax=5,gridlines='major')
p2.show()
#the roots of this function are 2.8 and -2.8
print('the roots of the function are 2.8 and -2.8')

#denote T
T(x)=(1/4*x+3/4)
print('T=',T)
#define plot number 3
p3=plot(T, -5,5, ymin=-5,ymax=5,gridlines='major')

#denote S
S(x)=(3-2*x)
print('S=',S)
#define plot number 4
p4=plot(S, -5,5, ymin=-5,ymax=5,gridlines='major')

#graph equation T and S
show(p3+p4)

print('The solution is (1,1)')