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2 years ago

Which of the following is a solution of the system 2x + y = 9 and 3x + 5y = 19.

Mathematics

1 answer:

Nezavi [6.7K]2 years ago

4 0

2x+y=9

3x+5y=19

I will do this problem in 2 ways. I.)Substitution II.)Elimination

Solution I.) Substitution

We can subtract 2x from both sides in the first equation.

y=9-2x

Now we can substitute the y in the second equation with 9-2x

3x+5(9-2x)=19

-7x+45=19

-7x=-26

x=26/7

y=9-2(26/7)=11/7

Solution II.)Elimination

We can multiply both side of first equation by 5 to get a 5y in both equations.

10x+5y=45

Now because both are positive 5y we just need to do simple subtraction of the 2 equation, each side respectively.

(10x+5y)-(3x+5y)=45-19

7x=26

x=26/7

2*26/7+y=9

y=11/7

Ultimately you get the same answer, both are viable methods, some problems are faster with one method but I recommend mastering both since they are very useful.

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A group of objects or numbers is called a A part of a set is called a

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Answer:

Set; subset.

Step-by-step explanation:

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A set can be made up of elements such as numbers, alphabets, people, cars etc.

<em>For instance, Set A = {2, 4, 6, 8, 10, 12} represents all the even number between 1 - 12.</em>

On the other hand, a subset is a part of a larger set.

<em>For instance, comedy movies, horror movies, romance movies, action movies are a subset of movies. </em>

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3 years ago

in January, Dawn earns $9.25 allowance. She earns 3 times as much in February. If during March, she earns $5.75 more than she di

AURORKA [14]

Jan: 9.25
Feb: 9.25 x 3 = 27.75
March: 27.75 + 5.75 = 33.50

Dawn earns $33.50

8 0

3 years ago

Read 2 more answers

Ella grew 3 over 4 of an inch last year. Ben grew 2 over 3 of an inch last year. How much more did Ella grow than Ben last year?

IrinaK [193]

Answer:

Ella grew $\frac{1}{12}$ of an inch more

Step-by-step explanation:

For this problem, you want to subtract Ben's growth from Ella's.

This expression would be $\frac{3}{4}$ - $\frac{2}{3}$ .

To work these out, they must have the same denominator (which should be the lowest common multiple or LCM).

In this case, the LCM is 12, so you want to multiply each side so the denominator is 12. This means the first fraction should be multiplied by $\frac{3}{3}$ and the second by $\frac{4}{4}$ .

This makes the expression $\frac{9}{12}$ - $\frac{8}{12}$ , which equals $\frac{1}{12}$ .

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3 years ago

Time to paint the living room. The room measures 20 feet wide by 30 feet long by 12

chubhunter [2.5K]

The cost to paint the walls and the ceiling is $855

First, we need to find the area that will be painted.

The area of two of the walls is:

A = 20ft*12ft = 240ft²

The area of the other two walls:

A' = 30ft*12ft = 360ft²

The area of the ceiling is:

A'' = 20ft*30ft = 600ft²

We also need to subtract the areas of the two doors and the 4 windows.

Each door is 7ft by 3ft, so the area of each door is:

a = 7ft*3ft = 21ft²

Each window is 4ft by 3ft:

a' = 4ft*3ft = 12ft²

Then the total area that will be painted is:

area = 2A + 2A' + A - 2a - 4a'

area = 2*( 240ft²) + 2*(360ft²) + 600ft² - 2*(21ft²) - 4*(12ft²)

area = 1,710 ft²

We know that we need two coats of paint to cover that area, and the cost per square foot of paint is $0.25, then the total cost is:

C = $0.25*2*(1,710) = $855

The cost to paint the walls and the ceiling is $855

If you want to learn more about areas:

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2 years ago

If 7 litres of petrol cost $14.70 ,calculate the cost of 15 litres of petrol<br><br> Kindly answer

erastovalidia [21]

Answer:

The cost of 15 liters is $31.50

Step-by-step explanation:

1. Find the price for 1 liter of petrol.

Divide the cost by the number of liters:

$14.70 / 7 = $2.10 per liter.

2. Multiply the price for 1 liter by the new number of liters, 15.

$2.10 per liter x 15 liters = $31.50

3 0

3 years ago

Which of the following is a solution of the system 2x + y = 9 and 3x + 5y = 19.​

Which of the following is a solution of the system 2x + y = 9 and 3x + 5y = 19.