SOLUTION: Solve. 3a - 12b - 2c = 5 4a - 3b + 8c = 5 6a + 9b + 16c = 4

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve. 3a - 12b - 2c = 5 4a - 3b + 8c = 5 6a + 9b + 16c = 4      Log On


   



Question 1203153: Solve.
3a - 12b - 2c = 5
4a - 3b + 8c = 5
6a + 9b + 16c = 4

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+3a+-+12b+-+2c+=+5.....eq.1
+4a+-+3b+%2B+8c+=+5.......eq.2
+6a+%2B+9b+%2B+16c+=+4......eq.3
-------------------------------
+3a+-+12b+-+2c+=+5.....eq.1.....multiply by 2
+6a+%2B+9b+%2B+16c+=+4......eq.3
-----------------------------------
+6a+-+24b+-+4c+=+10
+6a+%2B+9b+%2B+16c+=+4
-----------------------------------subtract
+6a+-+24b+-+4c+-%286a+%2B+9b+%2B+16c+%29=+10-4
+6a+-+24b+-+4c+-6a+-+9b+-+16c+=+6
+-+33b+++-+20c+=+6...solve for b
+-+6+++-++33b=20c
+c=-+6%2F20+++-+33b%2F20.........eq.1a


++3a+-+12b+-+2c+=+5.....eq.1
+4a+-+3b+%2B+8c+=+5.......eq.2.....multiply by 4
-------------------------------------------
+3a+-+12b+-+2c+=+5
+16a+-+12b+%2B+32c+=+20
-----------------------------------subtract
+3a+-+12b+-+2c-%2816a+-+12b+%2B+32c%29+=+5-20
+3a+-+12b+-+2c-16a+%2B+12b+-32c=+-15
+-13a++-34c=+-15....multiply by -1
+13a++%2B34c=+15.............solve for c
+c=+15%2F34-13a%2F34........eq.1b

from eq.1a and eq.1b we have

+-+6%2F20+++-+33b%2F20=15%2F34-13a%2F34...........solve for b
+b+=+130a%2F561+-+84%2F187......eq.1c

go to eq.1, substitute b and c

+3a+-+12%28130a%2F561+-+84%2F187%29+-+2%2815%2F34-13a%2F34%29+=+5.....eq.1.... solve for a
+3a+-+520a%2F187+%2B+1008%2F187+%2B13a%2F17+-+15%2F17=+5
+3a+-+520a%2F187+++%2B13a%2F17+=+5-1008%2F187%2B+15%2F17
+3a+-+520a%2F187+++%2B13a%2F17+=+5-1008%2F187%2B+15%2F17
+184a%2F187=92%2F187
+184a=92
+a=92%2F184
+a=1%2F2

go to

+b+=+130a%2F561+-+84%2F187......eq.1c, substitute a
+b+=+130%281%2F2%29%2F561+-+84%2F187
+b+=+-1%2F3

go to

+c=+15%2F34-13a%2F34........eq.1b, substitute a
+c=+15%2F34-13%281%2F2%29%2F34
+c=+1%2F4
solution:
+a=1%2F2
+b=-1%2F3
+c=1%2F4