Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. Hint: use addition property of equality and multiplication property of equality in your answers 5x + 2y = 7 3x - y = 2 A. To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations B. Why is this multiplication allowed? C. What variable will be eliminated when the equations are combined after the multiplication? D. Next, add the equations together. Your answer should be a single equation with one variable. E. Why can you add the equations? F. Solve the equation for x. G. Substitute x back into one of the equations to solve for y. H. What is the solution to the system of equations?

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

The system of two equations is:

[tex]5x+2y=7...(i)\\\\3x-y=2...(ii)[/tex]

Step A:

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations.

[tex]5x+2y=7\\\\6x-2y=4[/tex]

Step B:

The multiplication is performed to simplify the elimination process.

Step C:

The variable that will be eliminated when the equations are combined after the multiplication is y.

Step D:

Next, add the equations together. Your answer should be a single equation with one variable.

[tex]5x+2y=7\\ +\\6x-2y=4\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\11x=11[/tex]

Step E:

We can add the equation because both the equation are in the same format, i.e. ax + by = c.

Step F:

Solve the equation for x.

11x = 11

x = 1

Step G:

Substitute x back into one of the equations to solve for y.

[tex]5x+2y=7\\\\(5\times 1)+2y=7\\\\5+2y=7\\\\2y=7-5\\\\2y=2\\\\y=1[/tex]

Step H:

The solution to the system of equations is: (x, y) = (1, 1).


Related Questions

A busy traffic intersection in a city was experiencing an average of 20 accidents per week. The council decided to try to reduce the number of accidents by placing a stop sign at the intersection. In this situation, what is:

a. the null hypothesis
b. the alternative hypothesis

Answers

Answer:

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 > μ2

Step-by-step explanation:

We are told that the telraffic was experiencing an average of 20 accidents per week.

Thus, μ = 20

We are told that the council decided to try to reduce the number of accidents.

Thus defining the hypothesis, we have;

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 > μ2

HELP ME PLEASEEEEEEEEEEEEEEEE

Answers

The answer should be the second one 8 1/2

Olivia needs 54 licks for every 3 lollipops she eats.

Answers

18 is your answer

54 divided by 3 = eighteen

Answer:

If the question is how many licks does she need for each lollipop, the answer will be 18 licks

Step-by-step explanation:

54/3=18licks

Hope this helps pls give brainliest!

Jerry started doing sit ups every day. The first day he did 15 sit ups. Every day after he did 4 more sit ups than he had done the previous day. Today jerry did 65 sit ups. Write an equation that could be solved to find the number of days jerry has been doing sit ups, not counting the first day.

Answers

Answer:

y=4x+15

Step-by-step explanation:

y-total

x-days

write an equivalent multiplication expression for 1/3 divided by 3​

Answers

Answer:

1/3 times 1/3

Step-by-step explanation:

the answer is 1/3 * 1/3 because when you divide with fraction you make the 3 or 3/1 turned around which is 1/3, then you multiply 1/3 * 1/3

Determine whether the system has no, one, or infinitely many solutions.
y = -6
4x + y = 2​

Answers

Answer:

It should have one answer

Step-by-step explanation:

y = -6

4x + -6 = 2

4x = 8

2

Write two decimals that have the sum of 16.825

Answers

10.805 and 6.02


explanation: 10.805 + 6.02 = 16.825

What is the distance between $(12, 4)$ and $(5, 28)$?

Answers

Answer

8

Step-by-step explanation:

16

Using the distance formular, the distance between the coordinate points given is 25

Recall the relation :

Distance = √[(y2 - y1)² + (x2 - x1)²]

Distance = √[(28 - 4)² + (5 - 12)²]

Distance = √[(24)² + (-7)²]

Distance = √(576 + 49)

Distance = √625

Distance = 25

Hence, the distance between the points is 25

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write an equation of a line that passes through (-6,4) and is PERPENDICULAR to y=3x-11

Answers

Answer:

y = -1/3x + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Perpendicular lines have the negative reciprocal slope of the original.

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = 3x - 11

Point (-6, 4)

Step 2: Find slope m

Negative Reciprocal of 3 = -1/3

Step 3: Define

y = -1/3x + b

Step 4: Find y-intercept b

Substitute in point:                    4 = -1/3(-6) + bMultiply:                                      4 = 2 + bSubtract 2 on both sides:         2 = bRewrite:                                      b = 2

Step 5: Write perpendicular linear equation

y = -1/3x + 2

Tyler’s brother works in a shoe store. Tyler’s brother earns $12 per hour. The store offers him a raise—a 5% increase per hour. After the raise, how much will Tyler’s brother make per hour?

Answers

Answer: 12.6

Step-by-step explanation: calculator  ._.

Please tell me this answer

Answers

Answer: 162

60466176/373248

Step-by-step explanation: 12^4*9^3*4= 60466176 and 6^3*8^2*27= 373248. If you divide these together you get 128.

why does 4^3 equal 64 and not 12

Answers

Answer:

because 4.4.4.4

Step-by-step explanation:

If a number has an exponent it is not 4x3 it is 4x4x4. So if multiply four by itself three times you get 64. I hope that helps!

Plzz help....Calculate the length of the corresponding sides for FGHIJ and ABCDE. You will need to use the distance formula
[tex]d = \sqrt{x2 - x1) {2}^{?} } + (y2 - y1) {2}^{?} [/tex]
for sides that are not purely horizontal of vertical. Show your work in the table. Afterward, confirm your calculations using GeoGebra.

Answers

The distance between the points have been calculated.

What is the Distance Formula?

The distance formula is used to calculate distance between two points on a coordinate system.

The formula is

[tex]\rm d = \sqrt { (x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates of ABCD is A(0,4), B(2,4), C(2,3), D(4,2), E(4,0)

The coordinates of FGHI is F(7,1), G(6,1), H(6,1.5), I(5,2), J(5,3)

AB² =  (2-0)²+(4-4)²      

AB =     2

FG² =  (6-7)²+(1-1)²

FG =1                  

BC² =  (2-2)²+(3-4)²=1          

BC = 1

GH² =  (6-6)²+(1.5-1)²=0.5        

GH = 0.5

DI² =  (5-4)²+(2-2)²

DI = 1

HI² =  (5-6)²+(2-1.5)² = 1.25

HI =  1.12

DE² =  (4-4)²+(0-2)²

DE =    2

IJ² =  (5-5)²+(3-2)²

IJ = 1

EA² =  (0-4)²+(4-0)²      

EA = 5.66

JK² =  (7-5)²+(1-3)²    

JK =    2.83

The missing data of the question is

The coordinates of ABCD is A(0,4), B(2,4), C(2,3), D(4,2), E(4,0)

The coordinates of FGHI is F(7,1), G(6,1), H(6,1.5), I(5,2), J(5,3)

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What is the LCM of 81 and 84​

Answers

Answer:

2268

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of
Lake Michigan. The lake has a volume of about 4,920
_. Chicago was a major gateway to the west in
1825 when the Erie Canal was completed. When built,
the Erie Canal was 680 long and only 100_, or
10 deep. While in Chicago, Leon visited the Sear
Tower. One of the tallest buildings in the world, the
Sears Tower is 443 tall
during Leon's visit was about 7

Answers

Answer:

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of

Lake Michigan. The lake has a volume of about 4,920

km cubed. Chicago was a major gateway to the west in

1825 when the Erie Canal was completed. When built,

the Erie Canal was 680 long and only 100 or

10 deep. While in Chicago, Leon visited the Sear

Tower. One of the tallest buildings in the world, the

Sears Tower is 443 tall

during Leon's visit was about 7

A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or club a ​?

Answers

Answer: 0.3077

Explanation: In a standard deck of cards, there are 52 cards. They are broken down into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each. Each suit has 13 ordinal cards (A, 2 through 10, Jack, Queen, King).

Here we're asked to draw a card at random and find the probability of drawing either a diamond or a 7.

With probability, we look at the fraction of ways we can achieve some condition (the numerator) over the number of ways we can do something (the denominator).

Our denominator here is 52 - the number of cards from which we can pull 1.

Our numerator is both all the diamonds, 13 cards, and all the sevens, 4 cards, but we need to subtract 1 to account for the double counting of the 7 of diamonds.

In all we get: 13+4−1/52=16/52=4/13≈0.3077

Hope this helps... Stay safe and have a great day/night!!!

What is the easiest way to find the square root of a number?

Answers

Answer:

use a calculator

Step-by-step explanation:

best trick

You can memorize the basic square roots of the main numbers kinda hard but i guess that’s the only way after using a calculator

What is the kinetic energy of a bicycle that has a mass of 20 kg and is traveling at a velocity of 10 m/sec? KE= .5 x M x V^2

Answers

You have the formula.
KE= 0.5(20 kg) (10 m/s)^2
KE= 10kg * 100 = 1000 J

The kinetic energy of the bicycle is 100 N

What is kinetic energy?

Kinetic energy is the energy in motion and it is energy doing work. It can be expressed by using the formula:

[tex]\mathbf{K.E = \dfrac{1}{2}\times m \times v^2}[/tex]

where;

m = mass of the object v = velocity of the object

[tex]\mathbf{K.E =0.5 \times 20 \ kg \times 10 \ m/s^2}[/tex]

K.E = 100 N

Learn more about the kinetic energy here:

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Construct the exponential function that contains the points (0,3) and (2,75).

Answers

Answer: 3(5)^x

Step-by-step explanation:

that was the correct answer

The required exponential function is given as y = 3[5]ˣ.

What is an exponential function?

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Let
y = abˣ
Substitute the pairs and form two equations,
3 = a   - - - - - - - (1)
75 = ab²   - - - - - (2)

Dividing equation 2 by 1
25 = b²
b = 5
Now,
y = 3{5}ˣ

Thus, the required exponential function is given as y = 3[5]ˣ.

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When you [_______________] measurements, the answer should only have the same number of significant figures as the measurement with the fewest significant figures

Answers

Answer:

When doing multiplication or division with measured values, the answer should have the same number of significant figures as the measured value with the least number of significant figures. Procedure to determine significant figures after multiplication or division: 1.

Step-by-step explanation:

The required solution is multiplication or division.

It is required to find the fill in blanks.

What is arithmetic?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

When doing multiplication or division with measured values, the answer should have the same number of significant figures as the measured value with the least number of significant figures.

Therefore, the required solution is multiplication or division.

Learn more details about arithmetic here:

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please help me asap impor

Answers

I’m not sure sorry ☹️

the mean of the following numbers is 15. 14,10,18,,21,15,14​

Answers

Answer:

= 15.285714285714

Step-by-step explanation:

can someone help me round 621x29

Answers

Your rounded number is 18010

The reason for this is because when you multiply 621X29, you get 18009. When you round numbers, you want to see how the numbers are. If a number is 4 or below, you will make that number a zero or not count it, whereas numbers above 5 will go up. I hope this helps and if you have any questions, let me know

Answer:

18010

Step-by-step explanation: You see, 621x29=18009 and rounded is 18,010

The ratio of the number of silver watches to the number of gold watches in a shop 2:3. Which of the following best describes the number of silver and gold watches in the shop?

Answers

Answer:

For every 2 silver watches, there are 3 gold watches :)

Step-by-step explanation:

For every 2 silver watches, there are 3 gold watches :)

using the arithmetic sequence 12,15,18,21.....What is the 12th term of the sequence​

Answers

Answer: 45

Step-by-step explanation:

f(n) = f(1)+CD(n-1)

f(n) = 12+3(n-1)

f(n) = 12 +3n -3

f(n) = 3n+9

plug in 12 for n

f(12) = 3(12)+9

= 36 +9

=45

Answer: 45

Step-by-step explanation: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

(I'LL GIVE BRAINLIEST TO WHO EVER HELPS ME!!)

Estimate and then solve 6,699 ÷ 72 = ___.

A) 92 r 4
B) 93 r 3
C) 94 r 3

Answers

Answer:

C) 93 r 3

Your Welcome! ^O^

   0 0 9 3

7 2 6 6 9 9

 − 0      

   6 6    

 −   0    

   6 6 9  

 − 6 4 8  

     2 1 9

   − 2 1 6

         3

Answer:

thats wrong the correct answer is 94 r 3

Step-by-step explanation:

Select all radical expressions that are equivalent to 347. (3√4)7 (3√7)4 21−−√4 37−−√4 81−−√7 12−−√7

Answers

Answer: (3√7)4 and 81−−√7

Step-by-step explanation:

Find the value of x when x² is equal to 121. * 4 points

Answers

you would take the square root of x^2 and of 121 so x =11

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer
than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.
Which system of equations models this situation if the drummer wrote d songs and the
guitarist wrote g songs?

Answers

Answer:

Step-by-step explanation:

d + 2d - 8 = 46

3d - 8 = 46

3d = 54

d = 18

4 4/5 divided by 2 1/5​

Answers

Answer:

2 2/11

Step-by-step explanation:

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