How many solutions does each system have

Question

How many solutions does each system have?

System I:

x=y-3

 

2x-2y=-6


System II:

5x+2y=-7

 

15x+6y=21
 

is it

 

 

-System I has no solution and System II has an infinite number of solutions.

 

-Both systems have no solution.

 
-Both systems have an infinite number of solutions.

 
-System I has an infinite number of solutions and System II has no solution.
 
 
 

 
 
 

 
 
 
 
 
 

 
 
 

 
 
 

 

Answer 1

x=y-3   rewrite it as y=x+3

2x-2y=-6  rewrite it  2y=2x+6 then y=x+3

 

 

System 1 has infinite number of solution.  if you simplify you will see both are same equation. So they merge at each and every point.

 

5x+2y=-7    

y= -(5/2) x -7/2

15x+6y=21 rewrite it 

y=-(15/6)x+21/6

y=-(5/2)x + 7/2

Both have same slope -5/2

 

System 2 are parallel lines. Because their slope are same but y intercepts are  not same.  They will never intersect hence no solution