1.-Discuss and solve:
a) Independent system: x = 0, y = -3, z = 0
b) Dependent system: x = 2λ, y = λ - 3, z = λ, λ€R
c) Inconsistent system
d) Dependent system: x = z = λ, y = λ - 3; λ€R
2.- Discuss and solve:
a) Dependent system: x = y = λ, z = -λ; λ€R
b) Independent system: x = 3, y = z = -1
c) Independent system: x = y = 1, z = -1
d) Inconsistent system
3.- Discuss and solve:
a) Dependent system: x = λ + 1, y = 0, z = λ, λ€R
b) Independent system: x = 2, y = -2, z = 1
c) Independent system: x = -1, y = -2, z = 4
4.- Discuss and solve:
a) Independent system: x = 8, y = -6, z = 9
b) Independent system: x = 0, y = 2, z = 1
c) Dependent system: x = λ, y = λ - 2, z = λ, λ€R
5.- Discuss the following system depending on the value of the parameter a:
a) a = 1 dependent system; a ≠ 1 inconsistent system
b) a = -1 dependent system; a ≠ -1 inconsistent system
c) a = -1 independent system; a ≠ -1 inconsistent system
d) a = 1 independent system; a ≠ 1 inconsistent system
6.- Discuss the following system depending on the value of the parameter m:
a) Inconsistent system
b) m = 1 inconsistent system; m ≠ 1 dependent system
c) m = 1 inconsistent system; m ≠ 1 independent system
d) m = -3 independent system; m ≠ -3 dependent system
7.- Discuss the following system depending on the value of the parameter m and solve when it is possible:
a) m = 1 dependent system: x = -λ, y = 0, z = λ, λ€R; m ≠ 1 independent system: x = y = z = 0
b) m = -1 dependent system: x = -2λ, y = 0, z = λ, λ€R; m ≠ -1 independent system: x = y = z = 0
c) m = 3 dependent system: x = -4λ, y = λ, z = λ, λ€R; m ≠ 3 independent system: x = y = z = 0
d) m = 1 dependent system: x = 2λ, y = -3λ, z = λ, λ€R; m ≠ 1 independent system: x = y = z = 0
8.- Ben was in charge of ordering 26 pizzas for the office party. He ordered three types of pizza: cheese, pepperoni, and supreme. The cheese pizzas cost 6 € each, the pepperoni pizzas cost 9 €each, and the supreme pizzas cost 12 € each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If Ben spent a total of 222 € on pizza, how many pizzas of each type did he buy?
a) He bought 10 cheese pizzas, 12 pepperoni pizzas and 6 supreme pizzas
b) He bought 11 cheese pizzas, 10 pepperoni pizzas and 5 supreme pizzas
c) He bought 8 cheese pizzas, 13 pepperoni pizzas and 6 supreme pizzas
d) He bought 9 cheese pizzas, 12 pepperoni pizzas and 5 supreme pizzas
9.- The sides of a triangle are 26, 28 and 34 cm. Centered at each vertex are three circles, tangent to each other. Calculate the length of the radii of each circle.
a) 15, 17 and 21 cm
b) 13, 20 and 22 cm
c) 10, 16 and 18 cm
d) 14, 17 and 20 cm
10.- Joe's tire shop sells three types of tires. High performance tires sell for 40€/tire. Ultra performance tires sell for 60€/tire. Extreme performance tires sell for 80€/tire. Last week, the revenue generated by the sales of ultra performance tires exceeded the revenue from the sale of extreme performance tires by 560€. If the tire shop sold a total of 233 tires last week for a total revenue of 13.040€, how many of each type of tire were sold?
a) 90 high performance tires, 90 ultra performance tires, and 53 extreme performance tires were sold
b) 100 high performance tires, 80 ultra performance tires, and 53 extreme performance tires were sold
c) 90 high performance tires, 80 ultra performance tires, and 62 extreme performance tires were sold
d) 91 high performance tires, 90 ultra performance tires, and 63 extreme performance tires were sold
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