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vodomira [7]
2 years ago
15

Which of the following systems of equations has infinitely many solutions?

Mathematics
2 answers:
Sonja [21]2 years ago
3 0

Answer:

  • C. y = x + 4, 2y = 2x + 8

Step-by-step explanation:

The system has infinitely many solutions if the two equations are equivalent.

<u>We can analyze the given systems to see:</u>

A)

  • 2x + 7x + y = 6 ⇒ 9x + y = 6 ⇒ y = - 9x + 6
  • y = 9x + 6

Different slopes, there is one solution

B)

  • y = 5x + 7
  • y = 2x + 8

Different slopes, there is one solution

C)

  • y = x + 4
  • 2y = 2x + 8 ⇒ y = x + 4

Same lines, infinitely many solutions

D)

  • 7x - y = 10 ⇒ y = 7x - 10
  • y = 6x + 8

Different slopes, there is one solution

Ainat [17]2 years ago
3 0

Solution:

When two equations are equivalent, it is infinitely many solutions because the two lines overlap each other.

<u>Option A - 2x + 7x + y = 6 and y = 9x + 6</u>

  • => (9x + y = 6) = (y = 9x + 6)
  • => (y = -9x + 6) ≠ (y = 9x + 6)

<u>Option B - y = 5x + 7 and y = 2x + 8</u>

  • => (y = 5x + 7) ≠ (y = 2x + 8)

<u>Option C - y = x + 4 and 2y = 2x + 8</u>

  • => (y = x + 4) = (2y = 2x + 8)
  • => (y = x + 4) = (y = 2x/2 + 8/2)
  • => (y = x + 4) = (y = x + 4)

<u>Option D - 7x - y = 10 and y = 6x + 8</u>

  • => (7x - y = 10) = (y = 6x + 8)
  • => (-y = -7x + 10) = (y = 6x + 8)
  • => (y = 7x - 10) ≠ (y = -6x - 8)

Hence, Option C is correct.

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Answer:

D

Step-by-step explanation:

D

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3 0
3 years ago
Samantha is using a 2-liter pitcher to serve lemonade to 10 of her friends. How many times will she need to fill the pitcher in
Mice21 [21]

Answer: 2 times

Step-by-step explanation:

Hi, since 1000 milliliters = 1 liter

We have to convert the 2 liters into milliliters:

2 x 1000 = 2000 milliliters, so she is using a 2,000 milliliters pincher.

Now we have to multiply the number of friends (10) by the amount of lemonade she serves to each one (400 ml)

400 x 10 = 4,000 milliliters

Finally, we have to divide the amount of lemonade she needs to serve (4,000 ml) by the capacity of the pitcher (2,000), to obtain the number of times that she will need to fill the pitcher.

4,000/2,000=2 times

Feel free to ask for more if needed or if you did not understand something.

4 0
3 years ago
Read 2 more answers
A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?
N76 [4]
If the series is made up of numbers in an arithmetic progression, you have

\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185

where a_1 is the first term and d is the common difference between terms.

Since the last term in the series is a_{18}=275, you have

a_{18}=a_1+(18-1)d\implies a_1+17d=275

Solve the system

\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}

and you'll find that the first term is a_1=190 (with d=5).
5 0
4 years ago
HELP ASAP 10 POINTS TO BRAINLIEST
Brilliant_brown [7]

Answer:

15%

Step-by-step explanation:

The cost of 2 adults and 2 children without the discount is

2 adults = 2 (55) = 110

2 children = 2 (45) = 90

Total cost = 110+90 = 200

The original price is 200 and the new price is 170

Percentage discount = (Original price - new price)/ original price * 100%

                                     = (200-170)/200 * 100%

                                     = 30/200 * 100%

                                     = .15 * 100%

                                     = 15%

6 0
3 years ago
4x - 3y = k
Stella [2.4K]
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4 0
3 years ago
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