SOLUTION: 12. Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. 2x + 3y = 1 5x + 3y = 16

Solve each of the following systems by addition. 
If a unique solution does not exist, state whether the
system is inconsistent or dependent. 

2x + 3y =  1
5x + 3y = 16

To make the y's cancel, get the LCM of their coefficients
3 and 3 which is 3. Multiply the first equation through by 1
to keep 3y as it is.  Multiply the second equation through by
-1 to make it become -3y

 1[2x + 3y =  1]
-1[5x + 3y = 16]

Don't forget to multiply BOTH SIDES, not just the left side.

   2x + 3y =   1
  -5x - 3y = -16 

Now we add those vertically:

   2x + 3y =   1
  -5x - 3y = -16
 —————————————————
  -3x      = -15
         x = 5

2x + 3y = 1
5x + 3y = 16

To make the x's cancel, get the LCM of their coefficients 
2 and 5 which is 10. Multiply the first equation through by
5 to make 2x become 10x.  Multiply the second equation 
through by by -2 to make it become -10x

 5[2x + 3y =  1]
-2[5x + 3y = 16]

Afain, don't forget to multiply BOTH SIDES, not just the left side.

  10x + 15y =   5
 -10x -  6y = -32 

Now we add those vertically:

  10x + 15y =   5
 -10x -  6y = -32 
—————————————————
         9y = -27
          y = -3
 
Edwin
AnlytcPhil@aol.com