Solve each system of equations. See Example 2.
232 CHAPTER 4 Systems of Linear Equations
15.
1
2
x+
3
2
y+
3
4
z= 21
-
3
4
x-
1
3
y-
1
4
z= 3
1
3
x+
1
6
y-
2
3
z=- 1 16.
-
3
5
x+
4
3
y-
7
8
z=- 5
1
5
x+
2
3
y-
1
4
z=- 7
2
3
x-
1
4
y+
5
8
z= 0
17.
3.3x-7.5y+3.2z=21.25
2.2x+5.0y-0.1z=-5.97
5.5x-2.5y+1.6z=11.83 18.
9.3x-8.4y-4.8z=-34.20
3.1x+2.8y-0.2z=5.68
6.2x-1.4y+2.4z=-1.80
19.
2 y- z= 7
x+ 2 y+ z= 17
2 x- 3 y+ 2 z=- 1 20.
2 y+ z= 1
x+ 2 y- z= 8
2 x- y+ 3 z= 6 21.
x- 4 y+ z=- 4
4 x+ 2 y- 3 z= 6
22.
x- 6 y+ z=- 16
2 x+ 3 y- 4 z= 4 23.
3 x- 5 z=- 7
3 y- 2 z=- 4
2 x+ y= 6 24.
4 y+ z= 7
4 x- 8 y=- 7
25.
- x+ 6 y= 1
- 3 x- 2 y- z= 3
- 5 x+ 2 y+ z= 5 26.
- 2 x- 3 z= 12
- 5 x- 3 y+z=- 4
- 4 x+ 3 y-z= 4 27.
3
4
x+
1
6
y=- 2
2 y+ 4 z= 20
7 x- 3 z=- 34
28.
1
2
x+
2
3
y=- 1
4 y + 3 z=- 9
5 x - 2 z= 8 29.
1
3
x+
2
3
z=- 5
3
5
y+
1
2
z= 0
4 x - z=- 6 30.
1
5
y+
5
6
z= 4
2
3
y+
1
4
z=- 17
5 x- z= 38
Solve each system of equations. If the system is inconsistent or has dependent equations,
say so. See Examples 1, 3, 4, and 5.
31.
- x- y+ 3 z= 4
- 3 x+ y- z=- 2
2 x+ 2 y- 6 z= 5 32.
7 x+ 9 y- 2 z=- 5
5 x+ 14 y- z=- 11
33.
3 x- 3 y+ 12 z= 24
x- y+ 4 z= 8
3 x+ 12 y- 3 z= 9
x+ 4 y- z= 3
35.
3 x- y+ 5 z= 19
x+ 5 y- 2 z=- 1 36.
5 x+ 2 y+ 3 z=- 2
4 x+ y+ 2 z=- 4
x+ 3 y+ z= 2
37.
1
2
y+
1
2
z=- 3
4 x+ 2 y- 2 z= 12
2 x+ y- z= 6 38.
1
8
x-
1
2
y+
1
8
z=-
5
8
2 x- 8 y+ 2 z=- 10
39.
4 x+ 2 y- z= 0
3 x- y+ z= 0
x+ y- 2 z= 0 40.
3 x- 5 y- z= 0
x- 4 y+ 2 z= 0
2 x+ 3 y- z= 0
41.
3 x- 6 y+ z= 12
x- 2 y+
1
3
z= 4 42.
2 x+
1
2
y- z= 1
x+
1
4
y-
1
2
z=
3
4
4 x+ y- 2 z= 3
