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lisabon 2012 [21]
3 years ago
10

Which of the following systems has an infinite number of solutions?

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
3 0

Answer:

C. x+y = 1 and -x-y = -1

Step-by-step explanation:

Remember that if a system of equations has an infinite number of solutions, then the resulting equation from using the first step of the elimination method would have no variables and would be true.  

1) Let's try canceling out the equations in option C, x+y =-1 and -x-y =-1. Add the two equations together. (Work shown in attached picture.)

2) All of the terms cancel out with each other, leaving only a true statement of 0 = 0. Thus, option C is the answer.  

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Points A and B have coordinates (3,1,2) and (1,-5,4) respectively. Point C lies on line AB such that AC:BC=3:2. Find position ve
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Answer:

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Step-by-step explanation:

* Lets revise how to solve the problem

- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and

 point (x , y , z) divides the segment externally at ratio m1 :m2, then

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∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)

∵ Point C lies on line AB such that AC : BC=3 : 2

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 and AC : AB is m1 : m2

∴ x1 = 3 , x2 = 1

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∴ x=\frac{3(1)-2(3)}{3-2}=\frac{3-6}{1}=\frac{-3}{1}=-3

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∴ z=\frac{3(4)-2(2)}{3-2}=\frac{12-4}{1}=\frac{8}{1}=8

∴ The coordinates fo point c are (-3 , -17 , 8)

* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k

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