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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

how to see if matrix is one to one calculator

Answers

Answer:

look at the pivots (the leading 1's of the rows)

Step-by-step explanation:

Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.

16. The perimeter of a rectangular garden is 90 feet. The gardens lengin s5 feci less than 4 messen What are the length and width of the garden?​

Answers

9+10 equals whatever it was just the amount you paid and it didn’t even get to me until you were doing the right things I don’t

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]

If y is directly proportional to x and y is 12 when x = 10, what is y when x is 25?

Y = 25
Y = 30
Y = 20 5/6
Y = 26 1/5
None of the above

Answers

Answer:

Y= 30

Step-by-step explanation:

y=kx

when y=12, x=10

12=10k

k= 12/10

k = 6/5

when x= 25

y= 6/5 × 25

y= 30

simplify this equation

Answers

Answer: 3x/(x-3)(x+1)

please help me with this

Answers

Answer:

-9

Step-by-step explanation:

a(2) = a(1)+4 = -13+4 = -9

There are 25 students in Mr. Detwikers 1st period class. If 76% of these students complete their homework last night. How many students did their homework?

Answers

19 students did their hw

ITS DUE TMRW!! PLS HELP


What is the value of x in the solution to this system of equations?


5x − 5y = 120


y= −7x + 8


Enter your answer in the box.

Answers

Answer:

x  =  24  +  y

Step-by-step explanation:

Move all terms that don't contain  x  to the right side and solve.

Answer:

Step-by-step explanation:

5x − 5y = 120

y= −7x + 8

Use the second equation in the first (eliminates y)

5x − 5(−7x + 8) = 120

5x (+35x -40) = 120

40x -40 = 120

40x = 160

x = 4

----

If x = 4:

y= −7x + 8

y= −7*(4) + 8

y= -28 + 8

y = -20

====

The solution is (4,-20)

What is x? Show your work.

Answers

Answer: x=2

Step-by-step explanation: 28/4-5= 2

If Kenny attempted 36 serves yesterday, how many serves did he make over the net?

Answers

top diagram :) it’s a 7:2 ratio

Im just straight up confused. And dont leave a link

Answers

Answer:

The bottom left graph is a function

Step-by-step explanation:

I was pretty confused at first with this, too. To find if a graph is a function, however, just preform the vertical line test! Basically, draw a vertical line on each graph. At any point does it go through two or more points? Well, its not a function. We can see a vertical line would completly overlap the first graph, it would go through the half circle graph twice, and the circle? Well, that ones rather obvious...

With this test, we can see the only graph that passes the vertical line test is the bottom left graph (or the weird squiggly one)!

Hope this helps for future function solving!

C. I Believe! ( the bottom left corner )

Question 1
Without solving, what can you tell about the solution to
this equation?
b + 14
(b + 14)
2
1 / 116
There is no solution.
There are infinitely
many solutions.
b is equal to 1 only.
b is equal to 0 only.

Answers

Answer:

there are infinitely many solutions

Step-by-step explanation:

1/2(b+14) is the same as (b+14)/2, so no matter what number you plug in for b, both sides will always be equal. thus, there is infinitely many solutions.

hope this helps <3

Answer: there is no solution.

Step-by-step explanation:

We can see mentally that when we multiply both sides by 2, we will be left with b+14 on both sides which will cancel out ( “b” will cancel out) so there is no solution.

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify
any fractions.

15c + 11 + 6 = 17

15c + 17 = 17 (A : add 11 to both sides.
B : subtract 11 from both
sides.
C: multiply both sides
By 11.
D: divide both sides by
11.
E: combine like terms.

15c = ?

c = ?



Answers

Answer:

I can't understand what to do, so I hope this helps

15c=0

c=0/15 or c=0

Step-by-step explanation:

15c + 11 + 6 = 17

subtract 11 from both sides

15c + 6 = 6

subtract 6 from both sides

15c=0

divide both sides by 15

c=0/15

Alright I need help.. I will mark brainliest .
;-;

Answers

Answer:

  x - y = 9

Step-by-step explanation:

When x goes up by 1, y goes up by 1. That means there is a constant difference between the values. That difference is x1 -y1 = 1 -(-8) = 9.

An equation relating the values is ...

  x - y = 9

_____

Some folks like to see the relation in "y =" form. You can add y-9 to both sides to get that form:

  y = x -9

Can i get some help :

Answers

Answer:

is not equal to sign is used

If 3 is added to three quarter of a certain number, the result is 30.find the original number.

Answers

Answer:

Original number is 36

Step-by-step explanation:

Let,

Number be x

3x/4 + 3 = 30

3x + 12/4 = 30

3x + 12 = 30 × 4

3x + 12 = 120

3x = 120 - 12

3x = 108

x = 108/3

x = 36

Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l contains point S. The length of segment R S is 2 x + 8. The length of segment S Q is 8 x minus 4.
What is the length of segment SR?

Answers

Answer:

12

Step-by-step explanation:

Since RS = QS, we know 2x + 8 = 8x - 4

Subtract 2x from each side

8 = 6x - 4

Add 4 to each side

12 = 6x

Divide each side by 6

2 = x

SR is 2x + 8, so it is 2(2) + 8, so RS = 12

The length of the segment SR is 12.

What is a triangle?

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

Since RS = QS, we know 2x + 8 = 8x - 4

Subtract 2x from each side

8 = 6x - 4

Add 4 to each side

12 = 6x

Divide each side by 6

2 = x

SR is 2x + 8, so it is 2(2) + 8, SR = 12

Hence, the segment SR is 12.

To know more about triangles follow

https://brainly.com/question/17335144

#SPJ5

Triangles â–łABC and â–łDFG are similar. The lengths of the two corresponding sides are 1. 4m , and 56 cm. What is the ratio of the perimeters of these triangles ?.

Answers

Answer:

  5 : 2

Step-by-step explanation:

The ratio of perimeters of similar triangles is the same as the ratio of any pair of corresponding sides. That ratio is given as ...

  1.4 m : 56 cm = 140 cm : 56 cm = 5 : 2

The ratio of the perimeters of the triangles is 5 : 2.

_____

As a unit ratio, it is 2.5 : 1, or 2.5.

base five to decimal base

Answers

Answer:

Below.

Step-by-step explanation:

Here's an example.

What is 123 in base 5 converted to decimal.

123 base 5 =  3 * 5^0 + 2*5^1 + 1 * 5^2

= 3 + 10 + 25

= 38 in decimal.

Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffalo chicken sandwiches. How much does 12 burgers cost?

Answers

12 x $2.25 = $27.00 for twelve burgers.

Which of the following values could represent the probabilities of complementary events? StartFraction 1 over 7 EndFraction and StartFraction 2 over 7 EndFraction 28% and 82% Two-fifths and Three-fifths 10% and 80%

Answers

Answer:

a

Step-by-step explanation:

Answer:

2/5 and 3/5

Step-by-step explanation:

write y+9=-3x-9 in slope intercept form

Answers

Answer:

y = -3x - 18

Step-by-step explanation:

Subtract 9 from each side

when the angle of elevation of the sun is 78 degrees, an Statue casts a shadow that is 6m long. How far is the top of the statue to the end of it's shadow? ​

Answers

Answer:

28.9 m

Step-by-step explanation:

First, we can draw a picture. The statue is on the right, with the top of the statue representing the top right corner of the triangle. The angle of elevation to the sun is 78 degrees, so the angle between the shadow and the top of the statue must be 78 degrees as well. Assuming there is no angle of elevation between the shadow and the statue, we can say that the shadow and statue form a 90 degree angle because the shadow is perfectly horizontal and the statue is perfectly vertical.

We are trying to find the hypotenuse of the triangle, or the length from the top of the statue to the end of the shadow. To do this, we can utilize the fact that

cos(x) = adjacent / hypotenuse

cos(78°) = 6 / hypotenuse

divide both sides by cos(78°) and multiply both sides by hypotenuse to solve for the hypotenuse

hypotenuse = 6/cos(78°) ≈ 28.9 m

Graph: y =
|x – 4| + 2

Answers

This is a photo of answer

Answer:

  see attached

Step-by-step explanation:

The constants in the function shift the absolute value graph right 4 units and up 2 units. The attachment shows the translated function.

What are the other steps?

Answers

Answer:

63 degrees

Step-by-step explanation:

Angle IGH is 40 degrees because it is vertical to angle BGD.

Angle HIG is 77 degrees because it is a linear pair with CIH.

Since 2 of the angles of triangle GHI are 40 and 77 degrees, and the 3 angles add to 180, angle IHG must be 63 degrees

what is the value of k makes the equation trur

Answers

Answer:

where is the equation??

pls attach that

i will make you brainliest

Answers

Answer:

Answers given in the photo

3\sqrt{ }528
please help

Answers

Answer:

8.08248

Step-by-step explanation:

Use a calculator

What is the value of 24 + 32 - 52

Answers

The answer to you question is 4

What is the multiplicative rate of change of the
exponential function shown on the graph?
20
2,
81
4
16
0 1
12
4
9
8
9
1.
NI
(-2
. 81)-1,3
X
(0, 1)
1
2
Intro
Done

Answers

Answer:

  (d)  9/2

Step-by-step explanation:

The growth factor (multiplicative rate of change) can be found as the ratio of y-values for x-values that differ by 1.

Here, we have ...

  x = 0, y = 1

  x = 1, y = 9/2

These x-values differ by 1. The growth factor is (9/2)/1 = 9/2.

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