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Give two systems of equations that would be easier to solve by substitution than by elimination. Then give two systems that would be easier to solve with elimination. Finally, explain how you decide whether to use elimination or substitution to solve a system.

Answers

Answer 1

Answer:

These techniques for elimination are preferred for 3rd order systems and higher.  They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b.  Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method.  As the system of equations increases, the "condition" of a matrix becomes extremely important.  Some of this may sound completely alien to you.  Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n')  become larger than 2.

Step-by-step explanation:

Just to add a bit more information, "Elimination" Can have a variety of other interpretations.  Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.'  Do not worry if you have not heard of these terms.  They are used in Linear Algebra when referring to "Elimination techniques"

 

Gaussian Elimination

Gauss-Jordan Elimination

LU-Decomposition

QR-Decomposition

 

These techniques for elimination are preferred for 3rd order systems and higher.  They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b.  Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method.  As the system of equations increases, the "condition" of a matrix becomes extremely important.  Some of this may sound completely alien to you.  Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n')  become larger than 2.

 

Substitution is the preferred method for 2 equations in 2 unknowns.  The constants are unimportant other than having a non-zero determinant.  It is always easy to find multiplicative factors using LCMs of one variable or the other to allow substitution into the other equation:

 

Example:

 

4X + 5Y = 9

5X -  4Y = 1

 

Notice that 20 is a LCM of either the X or Y variable.  So multiply the first by 4 and the second by 5 and then adding the two (Y's will drop out allowing for substitution)

 

4(4X + 5Y = 9)

5(5X -  4Y = 1)  

 

Multiplying to produce the LCM factors:

 

16X + 20Y = 36

25X -  20Y = 5

 

Adding the equations

 

41X = 41

X = 1

 

Substitution into either equation yields

Y = 1

 

Elimination techniques are preferred for Rank-n>3

Answer 2

Answer:

I like the view


Related Questions

find 3 solutions that satisfy the equation -5x=10+2y

Answers

Answer:

(2, -10)

(4, -15)

(6, -20)

Step-by-step explanation:

First you should simplify the equation.

-5x=10+2y

-5x-10=2y

-2.5x-5=y

Then put in any number in for x. since we have a decimal I'll make the numbers I put in even the keep the solution whole numbers.

Putting in 2 gives you -10 so (2, -10) is a solution.

Putting in 4 gives you -15 so (4, -15) is a solution.

Putting in 6 gives you -20 so (6, -20) is a solution.

Pleaseeee help meee with this!!!!!!!!!!!!

Answers

Answer:

x=19

Step-by-step explanation:

The 2 angles are same side interior angles, so together they add to 180 degrees. So you can make this equation:

6x + 4 + 4x - 14 = 180

10x - 10 = 180 (Combine like terms)

10x = 190 (add 10 to each side)

x = 19 (divide both sides by 10)

These two angles add up to 180°

So just add them together and make them equal to 180°

6x + 4 + 4x - 14 = 180

Add like terms

10x - 10 = 180

10x = 190

x = 19

please show work

10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?

Answers

Answer:

34.2 m

Step-by-step explanation:

We know that

Area of parallelogram = Base × Height

690.84 = B × 20.2

690.84/20.2 = B

34.2 = B

Hence,

Base of parallelogram is 34.2 m

[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]

Here we've been given:

Area of parallelogram (A) = 690.84 m²

Height (H) = 20.2 m

Length of base (B) = ?

[tex]:\longrightarrow\tt{Area \: of \: parallelogram = Base \times Height} \\ \\ :\longrightarrow\tt{690.84 = B \times 20.2} \\ \\ :\longrightarrow\tt{ \frac{690.84}{20.2} = B} \\ \\ :\longrightarrow\tt{34.2 = B} \\ \\ :\longrightarrow\tt{B = 34.2 \: m}[/tex]

The length of base is 34.2m.

I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK

Answers

Answer:

√366

Step-by-step explanation:

a^2 + b^2 = c^2

5 + 361 = 366

√366

how to rewrite 3/4 with the denominator 12

Answers

9/12
Multiply 4 by 3 and multiply 3 by 3 and you get 9/12

Find the equation of a line that passes through the point (-4,1) and has a gradient of 2.
Leave your answer in the form
y=mx+c

Answers

Answer:

y = 2x + 9.

Step-by-step explanation:

Using the point-slope form:

y - y1 = m(x - x1)   where m = the slope and (x1, y1) is a point on the line.

So here we have:

y - 1 = 2(x - (-4))

y - 1 = 2(x + 4)

y - 1 = 2x + 8

y = 2x + 9.

Using a calculator or otherwise, calculate the exact value of 498.79×14.38. Round your answer to one (1) decimal place.

Answers

Answer:

7172.6

Step-by-step explanation:

Make x the subject of the formula: y=x^{2} + 5

Answers

First, multiply both sides by (x - 5), so you end up with:

(x-5)y = x + 2

Which can be expanded to give you:

xy - 5y = x + 2

Now add 5y to both sides to obtain:

xy = x + 2 + 5y

Now subtract x from both sides:

xy - x = 2 + 5y

Factorise x out:

x(y - 1) = 2 + 5y

Divide both sides by (y - 1):

x = 2 + 5y/y - 1

There you go, x is now the subject.

There are 34 carpenters in a crew. On a certain day, 29 were present. What percent showed up for work? (round to the nearest tenth)

Answers

Answer:

About 85.29 percent

Step-by-step explanation:

Recall that a percentage can also be represented as a proportion under 1; for example, 30 percent is .30 as a proportion of 1. So here we have 29 carpenters out of 34 that showed up, a ratio of .8529 showed up to work, and .8529 balance translates to 85.29 percent.

So 85.29 percent of the carpenters showed up to work.

I need help?????????

Answers

Answer:

3

Step-by-step explanation:

what is 2 + 2 + 2 +2 lol

Answers

Answer:

8 lol

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in ​21 minute? In ​1 hour?

Answers

15 3/4 miles in 21 minutes
45 miles in an hour
hope this is helpful!

PLZZ HELPPP!!!! I HAVE A EXAM TOMMOROW AND I HAVE TO FINSIH MY STUDY GUIDE..... AND I DONT KNOW THE ANSWERS PLZZZ HELP THE EXAM IS REALLLLLY IMPORTANT AND IS BASED ON WHETHER U PASS OR NOT AND AFFECTS UR GRADE BADLY!!!!!

Answers

Just focus I'm sure you will pass your exam :)

Would someone help me out?
A)56.6
B)58.4
C)53.5

Answers

Answer:

it is c

Step-by-step explanation:

Examples:

3x (coefficient is 3)

4t (coefficient is 4)

Review

Directions: Name the coefficient (s) in the following expressions:

1. 9s + 4t

2. 46rs + 10x

3. 18q + 14x

4. 10x + 14y

5. 17rs + 32x

6. 5x + 7y - 5z

7. 3ab + 70m

8. 3r + 20a + 10m

9. 7k + 16m

10. 7r + 5s

11. 9j + 120m

12. 12k + m

13. 6c + 15h + w

14. 2c - 19d + 12f

15. 3t + 14r - 31j

Answers

Answer:

1. 9 + 4

2. 46 + 10

3. 18 + 14

4. 10x+ 14

5. 17 + 32

6. 5 + 7- 5

7. 3 + 70

8. 3 + 20 + 10

9. 7 + 16

10. 7 + 5

11. 9 + 120

12. 12  

13. 6 + 15 +  

14. 2 - 19+ 12

15. 3 + 14 - 31

Step-by-step explanation:

yo can i get some help with this

Answers

Answer:

14

Step-by-step explanation:

Answer:

16 + 2 = 14 + 4

? = 14

Step-by-step explanation:

These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two blue marbles if the first one is placed back in

Answers

Answer:

2/9

Step-by-step explanation:

Use the SAS Postulate to prove triangle W X Y approximately equal to triangle W Z Y space i f space stack W Z with bar on top approximately equal to stack W X with bar on top space a n d space angle Z W Y approximately equal to angle X W Y.

Answers

In ∆WXY and ∆WZY,WX = WZ (given)Angle XWY = Angle ZWY (given)WY = WY (common)Therefore, by SAS congruency, ∆WXY is congruent to ∆WZY.

Hope you could get an idea from here.

Doubt clarification - use comment section.

12/15 =10/13 true or false

Answers

Answer:

False.

Step-by-step explanation:


PLEASE HELP! No phony answers, thanks! Happy holidays, Merry Christmas!!

Answers

Step-by-step explanation:

(f+g)(x) means we just add the 2 functions, so we have

(x-3) + 2x² = 2x² + x - 3

(f-g)(x) means we subtract g(x) from f(x), so we have

(x-3) - (2x²) = -2x²+x-3

Assuming that the dot signifies a multiplication sign and not a composition  sign, we have

(f*g)(x) = f(x) * g(x)

= (x-3) * 2x²

= 2x³ - 6x²

Plugging -2 in, we get

2(-2)³-6(-2)² = -16 -24 = -40

Calculate the volume of the storage tank to the nearest hundredth.
F.2,840.04 m3
G.8,520.12 m3
H.11,360.16 m3
J.34,080.47 m3

Answers

Answer:

gang gang shii

Step-by-step explanation:

gang gang.

A circle has diameter 18 inches, and a chord is 14 inches long. What is the distance in inches from the chord to the center of the circle, to the nearest hundredth?

Answers

Answer:

Let O be the center of a circle whose radius is r cm , in which AB= 14 cm long

cord is at a distanceof 24 cm from O. Draw a perpendicular OD on AB , thus ,

OD= 24 cm.

In right angled triangle. ODB

OB^2 = OD^2+ DB^2

r^2 =(24)^2+(AB/2)^2 = 576+(14/2)^2

r^2 = 576+ 49=625

r = √625. =25 cm. Answer.

In the diagram below, PQ and RS are parallel. Based on the angle measures in the diagram, what is the value of X?

Answers

Answer:

x would be equal to 70 grades

Step-by-step explanation:

The angle QRS is equal to 180 - 130 = 50 grades.

We add up that with the other 60 grades on the left, and we encounter ourselves with a simple equation:

60 + x + 50 = 180

x = 70

Hope this was helpful

The sum of half of a number and 49is 2 whole 1/4 of the number. find the number

Answers

Answer:

-93.5

Step-by-step explanation:

let the number be y

1/2 × y + 49 =2 1/4

y/2 +49 =9/4

y/2 =9/4-49

y/2 = 9-196/4

y/2 = -187/4

cross multiply

4y = -374

y = -93.5

Answer:

28

Step-by-step explanation:

Let the number is x

Half of a number = (1/2) x2 whole 1/4 of the number = (2 1/4) x = (9/4) x

The sum:

(1/2) x + 49 = (9/4) x(9/4)x - (1/2)x = 49(9/4 - 1/2)x = 49(7/4)x = 49x = 49 : 7/4x = 49 * 4/7x = 7 * 4x = 28

Find the length of OP.

Answers

Answer:

 OP = 84  

Step-by-step explanation:

The triangle is equilateral meaning all angles equal and all sides are equal.

5y - 6 = 4y + 12

y - 6 = 12

y = 12 + 6

y = 18

Now  

OP = 4y + 12

OP  =  4(18) +12

  OP = 84  

Jennifer competed in a race that included running and biking. She ran 134 miles and bicycled 3.6 miles. Her total time was 0.7 hour. What was her approximate average speed in miles per hour?

Answers

Answer:

not 100% but i think 196

Step-by-step explanation:

you go 134+3.6 then just divide by 0.7

I really really really need help with this

Answers

Answer:

404

Step-by-step explanation:

PEMDAS48 ÷ 6 + (5×6) × 13 + 6 =            → Parenthesis48 ÷ 6 + 30 × 13 + 6 =                → Multiplication, division8 + 390 + 6 =                              → Addition404

[tex]\huge \bf༆ Answer ༄[/tex]

Use PEDMAS/BODMAS rule for simplification !

Let's solve ~

[tex] \sf{48} \div 6 + (5 \times 6) \times 13 + 6[/tex]

[tex] \sf48 \div 6 + 30 \times 13 + 6[/tex]

[tex] \sf8 + 30 \times 13 + 6[/tex]

[tex] \sf8 + 390 + 6[/tex]

[tex] \sf404[/tex]

Holly spent a total of $28 to buy candy for his soccer team. He bought chocolate that cost $2 per bag and gummy that cost $3 per bag. There are 12 people on the team and each person only get one snack. x = bag of pretzel y = bag of chip
How many bars of chocolate did Holly buy?

Answers

Answer:

8 chocolate bars

Step-by-step explanation:


I think of a number, increase it by four and double the answer. The
result is 20 more than the number. Find this number.

Answers

Answer:

(x+4)2=x+20

2x+8=x+20

2x-x=20-8

x=12

The number I thought of is 12.

How to convert statements into numerical expressions ?

To convert statements into numerical expression break the statement into chunks write the terms with mathematical operations.Interpret twice, thrice, half of this etc logically.Practice a lot.

According to the given question I think of a number,Let the number be x.

I increase it by four and double (x+4)×2 = 2(x+4).

The result is 20 more than the number which is (x+20).

∴ 2(x+4) = (x+20)

2x + 8 = x + 20.

2x - x = 20 - 8.

x = 12.

learn more about numerical expression here :

https://brainly.com/question/14642484

#SPJ2

when x varies directly as 2y and x=6 when y=20 find y when x=9

Answers

Answer:

x=k×2y

substitute x for 6 and y for 20

6=2(20)×k

6=40k

Divide both sides by the coefficient of k

6/40=40k/40

3/20=k

To find y, when x=9

9=3/20×2y

9=6y/20

cross multiply

9×20=6y×1

180=6y

Divide both sides by the coefficient

y=30

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