The system of equations below has exactly one (x, y) pair for its solution.4x+6y=244x+6y=24
2x+y=82x+y=8
If we double each side of the second equation, 2x+y=82x+y=8, we have 4x+2y=164x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation.
If needed, you can support your explanation with hanger diagrams (upload a picture), or by inventing a situation that the equations represent.
If we add the two equations in the original system, we have 6x+7y=326x+7y=32. Explain why the same (x, y) pair is also a solution to this equation.
Again, you can support your explanation with diagrams or a situation, if needed.

Answers

Answer 1

Answer:

Final answer:

The equations are a system of linear equations. Modifying them through multiplication or addition while keeping both sides balanced doesn't change the solution. Any pair (x,y) satisfying one equation will satisfy the others.

Explanation:

In mathematics, these equations are a system of linear equations. This is essentially a set of two or more equations, with a common set of variables. The same pair (x, y) are the solutions for all equations, as the second equation is a simplified, scalar multiple of the first.

So, for the first original equation (4x + 6y = 24), and the modified one (4x + 2y=16) which is the second equation of the system doubled, we can see that the multiplier is the same for both the 'x' and 'y' on the left side, and the right side of the equation. Therefore, if a pair (x,y) has been found to satisfy the first equation, it will also work for the second, as essentially, the equations are equivalent.

Similarly, adding the original system of equations, we get 6x + 7y = 32. This also has the same solution set, just expressed differently. As long as you're performing the same operation (like doubling, adding etc.) to each side of the equations, the balance remains constant, retaining the same solution.

Learn more about System of Linear Equations here:

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Answer 2

Answer:

Answer:

7.9

Step-by-step explanation:

because you don't make sentence

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Solve the equation r+11+8r=29

Answers

Combine like terms: r+8r=9r. subtract 11 from both sides 9r=18. r=2

Ok so lets evaluate this equation. First,we have to combine like terms which in this case us r only. So lets do it r+8r is simply 9r+11=29 so now since we want to isolate or in other terms get r the variable by itself we would have to subtract 11 form both sides. 29 -11 is simply 18 now we have 9r=18 divide 9 on both sides and r is equal to 2

Simplify 1/2/5 please.

Answers

Answer:

0.1

Step-by-step explanation:

(1/2)/5 = 0.1

Answer:

Step-by-step explanation:

1/2 x 1/5 = 1/10

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.a. 8/9
b. 2

Answers

Hello,

Answer B
$a_(0)=-5\na_(9)=a_(0)+9*r\n13=-5+9*r\nr= (18)/(9)=2$

A rectangle measures 14cm by 4cm what is the area

Answers

Answer:

56 $cm^(2)$

Step-by-step explanation:

A rectangle measures 14 cm by 4 cm

Length of Rectangle= 14 cm

Breadth of Rectangle= 4 cm

Area of Rectangle= Length × Breadth

Area of rectangle= 14 cm× 4 cm

Hence,Area of rectangle = 56 $cm^(2)$

Hence, the correct answer is 56 $cm^(2)$

The answer is 56 so I am getting how many points?

In general, the median of a data set is less resistant to outliers than the mean. A. True B. False

Answers

A. true, the median of a data set is less resistant to outliers than the mean

Answer:

FALSE is the correct answer

Step-by-step explanation:

A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?Group of answer choices
A. No because an 117-foot ladder is needed but the truck has only a 95-foot ladder.
B. No because an 96-foot ladder is needed but the truck has only a 95-foot ladder.
C. Yes because only a 75-foot ladder is needed and the truck has a 95-foot ladder.
D. Yes because only a 91-foot ladder is needed and the truck has a 95-foot ladder.

Answers

Answer:

I guess the ans d is correct because using pythagoras theorem we get 91.26 ft .

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