SOLUTION: I have a math problem I cannot solve can somebody help me PLEASE! Determine whether the system has 1 solution,no solution,or many solutions: y=-x+2 3x+3y=6 and y=2/3x 2x-

I have a math problem I cannot solve can somebody help me PLEASE!
Determine whether the system has 1 solution,no solution,or many solutions:

First let's define a TOTALLY NUMERICAL EQUATION as an equation 
that contains no unknowns or variables, just numbers.

Here are some TRUE totally numerical equations:
"2 = 2", "-7 = -7", "0 = 0", "1000 = 1000"

Here are some FALSE totally numerical equations:
"5 = 3", "6 = -8", "0 = 1", "1000 = 999"

Rule: 

(1) Try to solve either by substitution or by elimination 
(addition or subtraction). 

(2) If you are successful in solving it, then the answer 
you get is the only solution, and therefore the system has 
ONE solution.

(3) If you are unable to solve it because it leads to a 
totally numerical equation, then

(4) If the totally numerical equation is TRUE, the system 
has MANY solutions.

(5) If the totally numerical equation is FALSE, the system 
has NO solutions.   


 y = -x + 2
 3x + 3y = 6

Try to solve by substitution:

Replace y in the second by -x+2 from the first:

3x + 3y = 6

3x + 3(-x + 2) = 6
3x - 3x + 6 = 6
          6 = 6

This is a totally numerical equation. It is true so there 
are MANY solutions.


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and 

y=2/3x
2x-y=-4

Clear the first one of fractions by multiplying by 3

3y = 2x
2x - y = -4

Solve the second equation for y

-y = -4 - 2x
 y =  4 + 2x

Substitute 4 + 2x for y in the first:

3y = 2x
3(4 + 2x) = 2x

12 + 6x = 2x
     4x = -12
      x = -3

y = 4+2x = 4 + 2(-3) = 4 - 6 = -2

So there is ONE solution  (-3,-2)

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Here is an example which has NO solutions:

 y = -x + 2
 3x + 3y = 7

Try to solve by substitution:

Replace y in the second by -x+2 from the first:

3x + 3y = 7

3x + 3(-x + 2) = 7
3x - 3x + 6 = 7
          6 = 7

This is a totally numerical equation. It is false so there 
are NO solutions.

Edwin
AnlytcPhil@aol.com