Use elimination to solve the system of equations given by 3x + 4y = 5 and 21x + 28y = 35.

(0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.

The correct option is (C).

To solve the system of equations using elimination, we'll manipulate one or both equations to eliminate one of the variables, either \(x\) or \(y\). Let's start by using elimination to eliminate \(x\).

Given the system of equations:

[tex]\[ \begin{cases} 3x + 4y = 5 \quad \quad \quad \quad \quad (1) \\21x + 28y = 35 \quad \quad \quad (2)\end{cases} \][/tex]

We can see that if we multiply equation (1) by 7, we can eliminate (x) when we add the equations together:

[tex]\[ 7(3x + 4y) = 7 \times 5 \][/tex]

[tex]\[ 21x + 28y = 35 \][/tex]

Now, we can rewrite equation (1) as:

[tex]\[ 21x + 28y = 35 \quad \quad \quad \quad \quad (3) \][/tex]

Now, we'll subtract equation (2) from equation (3):

[tex]\[ (21x + 28y) - (21x + 28y) = 35 - 35 \][/tex]

[ 0 = 0 ]

Since (0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.

So, the correct answer is option C: Infinitely Many Solutions.

complete question given below:

Use elimination to solve the system of equations given by 3x + 4y = 5 and 21x + 28y = 35.

A. No Solution

B. (5/3, 0)

C. Infinitely Many Solutions

D. (0, 5/4)

The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.

The area of this triangle, A, is equal to the perimeter of this triangle.

Create a system of equations to model this situation. Determine if there are any solutions, and, if possible, whether or not they are viable.

How many total possible solutions are there to this system?

Of any possible solutions, how many are viable solutions for this situation?

which questions are good examples of a statistical question? check all that apply

a. How many pets do you have

b. do you think a pet is a lot of work?

c. do you like having a pet?

d. how many times a day do you feed your pet?

e. do you feed your pet at night?

Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem. A cube-shaped bin has an edge length of 34 yard. What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box.

How many times can 3 go into 9

If the sles tax price je 162 and had a markdown of 1/4 what is the original price

find f when 27f=81 f=

If 5 lemons are used to make a gallon of lemonade,how many lemons are needed to make 3 gallons

Tickets are priced as follows:
Adult Tickets -£12
Child Tickets -£6
Cheryl rings the booking office to buy 6 adult tickets and 3 child tickets
She is told that a 10% booking fee will be added to the ticket price
2% will then be added if she is paying by credit card

Work out the total charge that Cheryl will have to pay if she uses her credit card to pay for the tickets

Pedro was simplifying four over seven divided by five over eight. and his work is shown below. Identify where he made his error. Original problem: four over seven divided by five over eight. Step 1: four over seven multiplied by eight over five . Step 2: four times five over seven times eight. Step 3: twenty over fifty-six. Step 4: five over fourteen.

What is the equation in point-slope form of the line passing through (2,2) and (4,8)

The arena intends to give a gift box to each company that hires a stand at the event. Select from the options below the nets which will fold up into a cube.

What is the product?
6(x – 1)^2
6(x^2 – 1)
(x + 1)(6x – 1)
(x – 1)(6x – 1)

Is this right. If so what’s the correct answer

If Mary deposits $275 in principal at an interest rate of 3.2 percent,how much interest will she earn in one year

45 brainliest pts.


Plz answer...

A right circular cylinder has a volume of 1296 cubic inches. If you divide the radius of the cylinder by 12, what would be the volume of the smaller cylinder?

if a + 8 = 11 what is the value of 8a

In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He figures he has time to make, at most, 25 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $675.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit? A. define variables B. Write the constraint inequalities that represent the situation, and explain what each of the inequalities represents. (You should have four inequalities.) C. What are the vertices of the feasible region?

Tennis balls are sold in tubes that hold 3 tennis balls each. A store stacks 2 rows of tennis ball tubes on its shelf. Each row has 7 tubes in it. How many tennis balls are there in all?

Ari bought a DVD that originally cost $15 on sale for 20% off. The sales tax is 5%. How much did Ari pay for the DVD, including tax.

how many square feet of outdoor carpet will we need for this hole

A chef mixed oil and vinegar to make a salad dressing she made enough dressing to fill 6 plastic bottles each bottle has 4/8 cup of olive oil and 2/8 cup of vinegar what was the total amount in cups of salad dressing the chef made?

At a concession stand, three hot dogs and two hamburgers cost $7.75;two hot dogs and three hamburgers cost $8.50. Find the cost of one hot dog and the cost of one hamburger

29 plus j is equal to the quotient of 77 and j

Write as an equation

Carl ran 27 miles last week. This is 3 times farther than Anna ran. Which equation can be used to find how many miles Anna ran?

PLEASE PLEASE HELP ME 25 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Washington longed to retire to his fields at Mount Vernon. But he soon realized that the Nation under its Articles of Confederation was not functioning well, so he became a prime mover in the steps leading to the Constitutional Convention at Philadelphia in 1787. When the new Constitution was ratified, the Electoral College unanimously elected Washington President.

Which provides the best objective summary of this excerpt?

A.)
Even though he was unanimously elected to be president, Washington wished he could retire to Mount Vernon instead.
B.)
The Constitution probably would not have been ratified if Washington had retired early at Mount Vernon instead of attending the Constitutional Convention.
C.)
Washington played a major role in the events that led to the ratification of the Constitution and was elected to be the country’s first president.
D.)
Even though he wished to retire, George Washington knew that the nation needed help, so he put a lot of effort into helping to develop the Constitution. Eventually, the Constitutional Convention took place in Philadelphia in 1787, and the Constitution was approved. Then, Washington was elected president of the country. The entire Electoral College voted for him.

Connie is a nurse and works a 12 hour shift if she worked 4 hours what fraction of her shift does she still have to work

PLEASE HELP ME I BEG YOU PLEASE PLEA PLEASE

Solve 2x + y + z = 5
4x – 2y – z = 0
3x – y + 2z = 6
(1, 1, 2)
(-1, -1, -2)
(5, 0, 6)
(1, 1, -2)

Solve 3x + 6y – 6z = 9
2x – 5y + 4z = 6
-x +16y + 14z = -3
(5, 0, 1)
(9, 6, -3)
(0, 3, 0)
(3, 0, 0)

Solve –x + y + 2z = 2
2x – y + z = 5
-4x – y + 3z = 3
(2, 5, 3)
(0, 4, -1)
(1, -1, 2)
(-1, 1, -2)

Solve –x + 3y + z = 9
2x + 5y = 27
3x + y – 2z = -18
(1, 3, -2)
(21, -3, 39)
(1, 2, -4)
(22, -1, 26)

Solve x – 2y – 3z = 3
3x + y + z = 12
3x – 2y – 4z = 15
(0, 0, -1)
(3, 12, 15)
(3, 9, -6)
(-3, -9, 6)

Solve x + 3y + z = 1
2x – y – z = 6
5x + y + z = 1
(1, 6, 1)
(1, 2, -6)
(2, 1, -4)
(-1, -2, 6)

Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles.

A popular brand of running shoes costs a local store $68 for each pair. If the store sells the shoes for $119, what is the percent of increase in the price?