5.｛7x+2y-z=7①6.{9x+4y+z=10①{6x-y+z=7②{-9x+2y+3z=-6②{4x+3y+z=9③{3x-4y+2z=5③x=1,y=1,z=2x=1,y=0,z=1

Question

5.｛7x+2y-z=7 ① 6.{9x+4y+z=10 ①
{6x-y+z=7 ② {-9x+2y+3z=-6 ②
{4x+3y+z=9 ③ {3x-4y+2z=5 ③
x=1,y=1,z=2 x=1,y=0,z=1

Answer 1

7x+2y-z=7 (1)
6x-y+z=7 (2)
4x+3y+z=9 (3)
(1)+(2)
13x+y=14 (4)
(1)+(3)
11x+5y=16 (5)
(4)×5-(5)
65x-11x=70-16
54x=54
x=1
y=14-13x=1
z=7x+2y-7=2
9x+4y+z=10 (1)
-9x+2y+3z=-6 (2)
3x-4y+2z=5 (3)
(1)+(2)
6y+4z=4
3y+2z=2 (4)
(2)+(3)×3
-10y+9z=9
10y-9z=-9 (5)
(1)×9-(2)×2
27y+20y=18-18
47y=0
y=0
z=(2-3y)/2=1
x=(5-2z+4y)/3=1