1.
|
a
|
x = 10 /11 y = 18 / 11 |
b
|
x = 4 y = 0 |
c
|
x = -1 y = 2 z = -3 |
|
d
|
x = 1 y = -5 c = 7 |
e
|
x = 3 y = -2 z = 2 |
f
|
p = 0.5 q = 0.3 r = 0 |
2. The equations are dependent, as one of the equations is derived from the other two.
3. Use elimination method as far as possible.
4. a. y = 1, x = 5.5
b. c = 10 (since then the equations are parallel but not coincident)
c. If the equations are consistent and distinct, then the corresponding lines are not parallel. Therefore they meet at one point, the unique solutions of the equations.
5. Cat food cost $1.82
Biscuits cost $1.92
Fruit cost $2.40
6. x = 3, y = -24, z = 30
7. a. 2.025 = 0.01p + 0.1q + r
2.9 = 0.04p + 0.2q + r
3.425 = 0.09p + 0.3q + r
b. s = -10
t = 8
u = 2
