Question 908961
5x−4y+3z=15
6x+2y+9z=13
7x+6y−6z=6 
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15x−12y+9z=45(mult. 1st eq. by 3)
6x+2y+9z=13(2nd eq.)
subtract:(eliminating z)
9x-14y=32(4th eq.)
..
10x−8y+6z=30(mult. 1st eq by 2)
7x+6y−6z=6(3rd eq)
add:(eliminating z)
17x-2y=36(5th eq.)
..
9x-14y=32(4th eq.)
119x-14y=252(mult. 5th eq. by 7)
subtract:(eliminating y)
-110x=-220
x=2
14y=9x-32=-14(4th eq.)
y=-1
3z=15-5x+4y=15-10-4=1(1st eq.)
3z=1
z=1/3
Check:x=2, y=-1, z=1/3
5x−4y+3z=10+4+1=15
6x+2y+9z=12-2+3=13
7x+6y−6z=14-6-2=6
check ok