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12. Solve each system of equations using elementary operations.
x
a. d.
3 y 4 z 1 x y z 0
1
x
3 y z 5
4 y 5 14
2 x y 1
5 z 2
x
5 y 3 21
3 z 3
4 7
b. 1 2x 3y z 6 e. 1 2x y 0
2
3
c. 1 x y 10
f.
2
3
x y 2z 31
x 2y z 17
y z 2
x z 4
2
3
1
2
3
2y z 7
2z x 0
x y 2z 13
2y 3z 12
x y 4z 19
A
T
13. A system of equations is given by the lines
L 1 : ax by p, L 2 : dx ey q, and L 3 : gx hy r.
Sketch the lines under the following conditions:
a. when the system of equations represented by these lines has no solutions
b. when the system of equations represented by these lines has exactly one
solution
c. when the system of equations represented by these lines has an infinite
number of solutions
14. Determine the solution to the following system of equations:
1
2
3
PART C
15. Consider the following system of equations:
1
2
x y z a
x y b
y z c
x 2y 1
2x k 2 y k
Determine the values of k for which this system of equations has
a. no solutions
b. an infinite number of solutions
c. a unique solution
NEL
CHAPTER 9 509