algebra 2 help?

Question

Solve each system of equations.
-10x - y + 8z = 170
x - 6y + 7z = -229
-x - 4y + 5z = -91

A x=-44, y=-10, z=-35
B x=-45, y=-14, z=-40
C x=38, y=22, z=-26
D x=-2, y=-7, z=1
E x=5, y=-4, z=9
F x=24, y=-19, z=41

Answer 1

The quick way is to try the various answers in each equation, and eliminate any answer which doesn't work for any equation. Answer (A) works for all three:

-10x - y + 8z = 170
-10(-44) - (-10) + 8(-35) = 170
440 + 10 - 280 = 170
170 = 170

x - 6y + 7z = -229
-44 - 6(-10) + 7(-35) = -229
-44 + 60 - 245 = -229
-229 = -229

-x - 4y + 5z = -91
-(-44) - 4(-10) + 5(-35) = -91
44 + 40 - 175 = -91
-91 = -91

Answer (B), for example, is ruled out by the second equation:

x - 6y + 7z = -229
-45 -6(-14) + 7(-40) = -229
-45 + 84 - 280 = -229
-241 = -229

Answer 2

x - 6y + 7z = -229
-x - 4y + 5z = -91
-----------------------
-10y + 12z = -320
z = (-320+10y)/12


-10x - y + 8z = 170
(x - 6y + 7z = -229) (10)
10x -60y +70z =-2290
---------------------------------
-61y +78z = -2120
-61y +78(-320+10y)/12 = -2120
-61y - 24960/12 +780x/12 =-2120
-61y -2080 +65x =-2120
-61y +65y=-2120+2080
4y=-40
y= -10

A x=-44, y=-10, z=-35

Answer 3

-10x - y + 8z = 170
x - 6y + 7z = -229
-x - 4y + 5z = -91
****************
Equation 1: -10x-y+8z=170
Equation 2: x-6y+7z=-229 (10)
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Equation 1: -10x-y+8z=170
Equation 2: 10x-60y+70z=-2290
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Equation 4: -61y+78z=-2120
************************************
Equation 2:x-6y+7z=-229
Equation 3: -x-4y+5z=-91
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Equation 5: -10y+12z=-320
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Equation 4: -61y+78z=-2120(10)
Equation 5: -10y+12z=-320(-61)
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48z=-1680
z=-35
Since only one answer has z=-35, the
ANSWER:A