Systems of Equations - Solutions (Graphing & Substitution)

  When solving systems of
 equations, you have three
 types of possible solutions.
      Solutions to
Systems of Equations 
One Solution....
   This is when you
 are able to solve the
 equations to find the
value of each variable. 
(x,y)
One solution....
        In a graph                        In substitution
Point of intersection
         is (2 , 7)
so
the system has ONE solution....
You are able to use substitution
to find the value of both variables
      ie:  x = 2     &    y = 7 
(2,7)
No Solutions....
 When solving, the variables    are canceled out leaving   two DIFFERENT numbers.
This is when you are unable
to solve the equations to find 
  the value of each variable. 
         Parallel lines
No point of intersection.
No solution....
        In a graph                        In substitution
so
the system has NO solution....
     When using substitution,
you are unable to find the value of the variables...they cancel outto leave two DIFFERENT numbers... 
      ie:   2 = 7 
             ....an untrue statement
Infinitely Many Solutions..
 When solving, the variables    are canceled out leaving       the SAME numbers.
This is when you are unable
to solve the equations to find 
  the value of each variable. 
Infinitely Many Solutions..
         The SAME LineNo point of intersection.
so
        In a graph                        In substitution
the system has
    INFINITELY MANY solutions...
     When using substitution,
you are unable to find the value of the variables...they cancel outto leave the SAME numbers... 
      ie:   7 = 7 
             ....an true statement
What is the solution to the following system of equations?
Solve by graphing.
y = 3x + 6y = - x + 2
 (-1,3)
No Solution
Infinitely Many
       Solutions
What is the solution to the following system of equations?
Solve by graphing.
y = 4x + 4y = 4x + -1
Infinitely Many
       Solutions
(-1,4)
No Solution
What is the solution to the following system of equations?
No Solution
Infinitely Many
        Solutions
(-1,-2)
Solve by substituting.
y = 2x - 16x - 2y = 2
What is the solution to the following system of equations?
No Solution
Infinitely Many
        Solutions
(4,3)
Solve by substituting.
2x - 5 = y-1 + x = y 
What is the solution to the following system of equations?
(4,10)
No Solution
Infinitely Many
        Solutions
Solve by substituting.
y = 2x - 24x - 2y = 10
Let's Review....
When a system of equations has infinitely many
solutions, the solution looks like            and the graphed lines are                .
When a system of equations has no solution,
the solution looks like           and the graphed lines are                    .
When a system of equations has one solution,
the solution looks like            and the graphed lines                     .
use the numbers 3 and 8 to
answer the following questions
and DO NOT skip spaces
     After completing this review,what is your level of understanding?
Rating Scale:
    4 - I understand it and can teach it    3 - I understand it    2 - I can do it with more practice/the use of my notes     1 - I still don't understand
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