Question 412115
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Hi, Sry, can't help with the tables referenced...however:
Solving the following systems by elimination:
X+Y=9
X+2Y=13

-X-Y= -9  |multiplying 1st Eq thru by -1, adding to eliminate X
 X+2Y=13
   Y = 4  and X = 5
3X+7Y=24
9X+5Y=24

-9X-21Y=-72 |multiplying 1st Eq thru by -3, adding to eliminate X
 9X+5Y = 24
   -16Y =-48
      Y = 3 and X = 1

4X+Y=17
2X+3Y=21

 4X+Y=17
-4X-6Y=-42 |multiplying 2nd Eq thru by -2, adding to eliminate X
   -5Y = -25
     Y = 5  X = 3  (4X = 12 from 1st Eq)

18X+Y=42 
6X-3Y=-6

 18X +Y=42 
-18X+9Y=18   |multiplying 2nd Eq thru by -3, adding to eliminate X
     10Y = 60
       Y = 6  and X = 2 (18X = 36 from 1st Eq)


X+Y=5
X+Y+2Z=5  Z = 0   |as X + Y = 5
X+3Y+Z=11

  X +Y = 5
 -X -3Y = -11  |multiplying 3rd Eq thru by -1, adding to 1st Eq to eliminate X
    -2Y = -6
      Y = 3 and X = 2  
7) with the same solution as #5 |Eqs are multiples of one another
6) X = 2    Y = 5   Z = 0

Wishing You ALL the best!