SOLUTION: Solve by elimination {21x-7y+51z=141 13x+9y-5z=-19 19x-8y+23z=30

Question 536403: Solve by elimination
{21x-7y+51z=141
13x+9y-5z=-19
19x-8y+23z=30
Found 2 solutions by Alan3354, mananth:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x = -2
y = 3
z = 4
---------
That's too ugly to do by elimination.
If you have to, you can check your answers.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
21 x + -7 y + 51 z = 141 -------------- 1
13 x + 9 y -5 z = -19 -------------- 2
19 x + -8 y + 23 z 30 -------------- 3

consider equation 1 &2 Eliminate y
Multiply 1 by 9
Multiply 2 by 7
we get
189 x + -63 y + 459 z = 1269
91 x + 63 y + -35 z = -133
Add the two
280 x + 0 y + 424 z = 1136 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 8
Multiply 3 by 9
we get
104 x + 72 y + -40 z = -152
171 x + -72 y + 207 z = 0
Add the two
275 x + 0 y + 167 z = -152 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -275
Multiply (5) by 280
we get 2
-77000 x + -116600 z = -312400
77000 x + 46760 z = -42560
Add the two
0 x + -69840 z = -354960
/ -69840
z = 5.08 OR 5 8/97

Plug the value of z in (5)
275 x + 848.77 = -152
275 x = -1000.77
x = -3.64 OR -3 62/97
plug value of x & z in 1
-76.42 + -7 y + 259.21 = 141
-7 y = 76.42 + -259.21 + 141
y = 5.97 OR 6
CHECK
Plug values of x,y,z in (2)

13 -3.64 + 9 5.97 -5 5.08 = -19
m.ananth@hotmail.ca
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