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g100num [7]
3 years ago
11

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 5x+7=2y and

y-9x=23
A) {}
B) 1 solution
C) Infinite
Mathematics
2 answers:
Luda [366]3 years ago
7 0

Answer:

The correct option is option B. It has one solution, and it's x=-3

Step-by-step explanation:

We have the following system of equations:

5x+7 = 2y                        (1)

y-9x=23                            (2)

Step 1: Solve for 'y' in equation (2):

y-9x = 23

y = 9x + 23

Step 2: Substitute in equation (1):

5x + 7 = 2y

5x + 7 = 2(9x + 23)

5x + 7 = 18x + 46

Step 3: Solve for x:

7 - 46 = 18x - 5x

-39 = 13x

x= -3

So the correct option is option B. It has one solution, and it's x=-3

jeka57 [31]3 years ago
7 0

Answer: Option B

The system has 1 solution

Step-by-step explanation:

We must solve the following system of equations

5x+7=2y\\\\y-9x=23  

To solve it, clear y from the second equation and then substitute in the first equation

y=23 + 9x

Now substitute in the first equation

5x+7=2(23 + 9x)\\\\5x +7 = 46 + 18x\\\\5x -18x = 46-7\\\\-13x = 39\\\\x = -\frac{39}{13}\\\\x=-3

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12345 [234]

Answer:

1) G(t) = 75 + \frac{23}{4}t\\

2) After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

Step-by-step explanation:

1) For generating the equation we have to take into account that in the tanks there is a initial volume of fuel that corresponds to 75 gallons, as it is stated that tank one is half full. As the capacity for tank 1 is of 150 gallons, half of the tank equals to:

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Now we have to convert the rate of delivery that is expressed as a mixed number to an improper fraction so:

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Then the pumping rate is of 23/4 gallons per minute, to get how many gallons are in the tank we just need to multiply this rate by the time in minutes, and as there is an initial volume we have to add it, so we have the following equation:

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2) To know how much fuel is in the tank after 8 minutes we have to replace this time in the previous equation so we have

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3 years ago
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