Can you please help me solve this system of equation 
using the substitution and elimination methods. 

 8x + 9 = -5y
-3x + 3y = -21

Rules for the substitution method:

1. Solve either equation for either letter.  Call the letter you picked
   the "first" letter.You'll get an expression, not a numerical value, 
   for the first letter.  That expression will contain the other letter,
   which we call the "second" letter.

2. Substitute the expression you get for the first letter in the OTHER 
   equation.

3. Solve for the value of the second letter. You'll get the actual value 
   for the second letter.  

4.  Substitute that value for the second letter in either equation.

5. Solve for the first letter.  You'll get the value of the first letter.  



 8x + 9 = -5y
-3x + 3y = -21

1. Let's choose the bottom equation and choose the first letter as y.
   We solve for y:

   -3x + 3y = -21
   +3x            + 3x
  -------------------
         3y = -21 + 3x

Divide every term by the coefficient of y, which is 3:

       3y/3 = -21/3 + 3x/3

          y = -7 + x

2. Substitute the expression (-7 + x) for y in the top equation 

     8x + 9 = -5y
     8x + 9 = -5(-7 + x)

3. Solve for x
     8x + 9 = 35 - 5x

     8x + 9 = 35 - 5x
         -9   -9
    ---------------------
     8x     = 26 - 5x
    +5x          + 5x  
  -------------------------
    13x     = 26

   Divide both sides by 13

     13x/13 = 26/13
          x = 2

4.  Substitute x = 2 in either of the original
    equations.  I'll arbitrarily pick the first 
    one:
    
     8x + 9 = -5y
   8(2) + 9 = -5y
     16 + 9 = -5y
         25 = -5y

Divide both sides by -5
         
    25/(-5) = -5y/(-5)
         -5 = y
          y = -5

So now we have the solution: (x, y) = (2, -5) 

------------------------------------------------------

Rule for the elimination method:

1. Choose a letter to eliminate, call it the "first" letter.
2. Arrange the equations so that the corresponding terms are
   lined up vertically.
3. Find the LCM of the absolute values of the two coefficients
   of the first letter.
4. Multiply each of the two equations respectively through by 
   whatever pair of numbers will cause the two coefficients to 
   have the same absolute value but opposite in sign.
5. Add term-by term vertically. You will get an equation in
   only the second letter.
6. Solve for the second letter.
7. You have a choice here:
    (a) Substitute the velue of the second letter in either 
        equation to find the value of the first letter

     OR
    (b) Start over with step 1 but this time choose the other
        letter to eliminate.

 8x + 9 = -5y
-3x + 3y = -21

1.  Arbitrarily choose x to eliminate:

2.  Line up the equations vertically like this:

    8x + 5y = -9
   -3x + 3y = -21

3.  The LCM of 8 and 3 is 24. 

4.  Multiply the first equation through by 3 and 
    the second through by 8

    3[  8x + 5y = -9  ]
    8[ -3x + 3y = -21 ]   
  
      24x + 15y =  -27
     -24x + 24y = -168

5. Add term-by term vertically:

      24x + 15y =  -27
     -24x + 24y = -168
   -----------------------
            39y = -195

6.  Solve for y: 
            39y = -195

    Divide both sides by 39
              y = -5

7.  I'll choose to start over.

 8x + 9 = -5y
-3x + 3y = -21

1.  This time I choose y to eliminate:

2.  Line up the equations vertically like this:

    8x + 5y = -9
   -3x + 3y = -21

3.  The LCM of 5 and 3 is 15. 

4.  Multiply the first equation through by 3 and 
    the second through by -5

    3[  8x + 5y = -9  ]
   -5[ -3x + 3y = -21 ]   
  
      24x + 15y = -27
      15x - 15y = 105

5. Add term-by term vertically:

      24x + 15y = -27
      15x - 15y = 105
   -----------------------
      39x       =  78

6.  Solve for x: 
            39x = 78

    Divide both sides by 39
              y = 2

So now we have the solution: (x, y) = (2, -5)

Edwin