SOLUTION: What are the solutions to 6x+3y+z=19 x-3y+2z=21 17x-2y+3z=86

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Question 445381: What are the solutions to
6x+3y+z=19
x-3y+2z=21
17x-2y+3z=86
Found 3 solutions by mananth, ikleyn, MathTherapy:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
6x+3y+z =19--------------1
x-3y+2z=21--------------2
17x-2y+ 2z=86-----------3

consider equation 1 &2 Eliminate y
Add the two
7x+3z=40-------------4
consider equation 2 & 3 Eliminate y
7x+3z=40--------------5
Multiply 2 by -2
Multiply 3 by 3
we get
-2x+6y-4z=-42
51x-6y+ 6z=258
Add the two
49x+2z=216 -------------5 5
Consider (4) & (5) Eliminate z
Multiply 4 by -7
Multiply (5) by 1
we get
-49x-21z=-280
49x+2z=216
Add the two
-19z=-64
/-19
z=3.37
Plug the value of z in 5
49x+6.74=216
49x=209.26
x=4.27
plug value of x & z in 1
25.62+3y+3.37=19
3y=-25.62-3.37+ 19
y=-9.99

m.ananth@hotmail.ca

Answer by ikleyn(53419)   (Show Source):
You can put this solution on YOUR website!
.
What are the solutions to
6x+3y+z=19
x-3y+2z=21
17x-2y+3z=86
~~~~~~~~~~~~~~~~~~~~~

The solution in the post by @mananth x = 4.27, y = -9.99, z = 3.37 is incorrect.

To check, I substituted these values into first equation and got the value of the left side -0.98,
different from 19.

This is just enough to refute the solution by @mananth.

If you want to get a precise solution, go to website https:\\www.reshish.com/
Find there free of charge solver and use it.
The solver can provide step-by-step procedure with all necessary detailed explanations.

Answer by MathTherapy(10586)   (Show Source):
You can put this solution on YOUR website!

What are the solutions to 6x+3y+z=19 x-3y+2z=21 17x-2y+3z=86 6x + 3y + z = 19 ----- eq (i) x - 3y + 2z = 21 ----- eq (ii) 17x - 2y + 3z = 86 ----- eq (iii) 7x + 3z = 40 ----- Adding eqs (i) & (ii) --- eq (iv) 2x - 6y + 4z = 42 -- Multiplying eq (ii) by 2 --- eq (v) 51x - 6y + 9z = 258 -- Multiplying eq (iii) by 3 -- eq (vi) 49x + 5z = 216 ---- Subtracting eq (v) from eq (vi) ----- (vii) 49x + 21z = 280 ---- Multiplying eq (iv) by 7 --- eq (viii) 16z = 64 ---- Subtracting eq (vii) from eq (viii) 7x + 3z = 40 ---- eq (iv) 7x + 3(4) = 40 ---- Substituting 4 for z in eq (iv) 7x + 12 = 40 7x = 28 x - 3y + 2z = 21 ----- eq (ii) 4 - 3y + 2(4) = 21 ----- eq (ii) --- Substituting 4 for x, and 4 for z in eq (ii) 4 - 3y + 8 = 21 - 3y + 12 = 21 - 3y = 9