{x + y = 9, 1/x + 1/y = 1/2} Find x and y.

leads to

but 
so

this means


which leads to


so that  or 
then we can see:
{ (3,6), (6,3) }

1...The square difference of two numbers is 25 and the twice of the first is 1 greater than the second. Find the two numbers

1) (x-y)^2=25
2) 2x=y+1 


y=2x-1 
so that

(x-(2x-1))^2=25 

which leads to: 

x={-4, 6} 
y={-9, 11} 

solutions: {(-4,-9), (6,11)}

Solve: {x+y^2=4 ,x^2+y^2=16}

 

 
therefore 
 
so that 
 

x=4 or x=-3 

x=-3 leads to  or  
x=4 leads to  

Solve each system by substitution method 1) y=x^2+6x+9 2) x+y=3

y=3-x 
y=x^2+6x+9 

leads to

3-x=x^2+6x+9 

x^2+7x+6=0 
(x+6)(x+1)=0 

x=-1 or x=-6


:)