Can somebody give me an review over how to solve systems of equations by substitution and elimination? PLEASE HELP I forgot how to do it and my Algebra EOC is TOMORROW!! I provided an example question and I need LONG ACCURATE and HELPFUL explanations, not a one sentence response (or I will report you). PLEASE HELP ME!!!

Can Somebody Give Me An Review Over How To Solve Systems Of Equations By Substitution And Elimination?

Answers

Answer 1

Answer:

Price per large envelope = $1.42 (option A)

Price of each postcard = $0.35 (not asked for in this specific question)

Step-by-step process for solution given below

Step-by-step explanation:

The first thing to do for this problem and other similar problems is to set up the system of linear equations to be solved

We start with the unknowns and provide variable names for these unknowns

There are two unknowns here - the cost of each postcard and the cost of each large envelope

Let
x = cost of one postcard

y = cost of one large envelope

Customer 1 bought 14 postcards(cost = 14x) and 5 envelops(cost = 5y) for a total cost of $12

We can set up this as an equation:
12x + 5y =  12    ............ [1]

Customer 2  bought 10 postcards(cost = 10x) and 15  envelops(cost = 15y) for a total cost of $24.80
This translates to the following equation:
10x + 15y = 24.80 .... [2]

Let's re-write these equations one below the other for easier solution:

[tex]\begin{amatrix}14x+5y=12\dots[1]\\ 10x+15y=24.8\dots[2]\end{amatrix}[/tex]

Solving by substitution:
From any one of the above equations, express one variable in terms of the other variable and substitute for that variable in the other equation to solve.

Take equation [1]
[tex]14x+5y=12[/tex]

Let's express x in terms of y.

Move 5y to the right:
[tex]14x=12-5y[/tex]

[tex]x =\dfrac{12-5y}{14}[/tex]

Use this expression in y for x in equation [2]

[tex]10x + 15y = 24.8\\\\\implies 10 \cdot \dfrac{12-5y}{14}+15y=24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\[/tex]

Multiply throughout by 14:
[tex]14 \cdot \dfrac{\left(12-5y\right)\cdot \:10}{14} + 14\cdot 15y = 14 \cdot 24.8\\\\(12-5y)10 + 210y = 347.2\\\\120 - 50y + 210y = 347.2\\\\120 + 160y = 347.2\\\\160y = 347.2- 120\\\\160y = 227.2\\\\y = \dfrac{227.2}{160}\\\\y = 1.42[/tex]

Substitute y = 1.42 in equation [tex]x=\dfrac{12-5y}{14}[/tex]
[tex]x=\dfrac{12-5\cdot \:1.42}{14}\\\\x = 0.35\\\\[/tex]

So the cost of each large envelope was $1.42 and cost of each postcard was $0.35

Answer is option A

Solve by elimination

The idea here is to get the coefficients of one of the variables the same in both equations by multiplying / dividing one or both of the equations by some factor and then add/subtract to isolate the other variable and solve


For equations 1 and 2 do the following

Multiply 14x+5y=12 by 5 :      70x+25y=60Multiply 10x+15y=24.8 by 7 :      70x+105y=173.6

Subtract the equations:
[tex]70x+105y=173.6\\-\\70x+25y=\;\;\;\;\;60\\\\[/tex]
-------------------------------
[tex]80y=113.6[/tex]

y = 113.6/80 = 1.42 as before

Substitute for y in equation 1 and solve for x
14x + 5y = 12 => 14x + 5(1.42) = 12

=> 14x + 7.1 = 12

=> 14x = 12 - 7.1

=> 14x = 4.9

=> x = 4.9/14 = 0.35 as before

I personally prefer solving by elimination since solving by substitution involves heavy duty fractional expressions




Related Questions

PLEASE HELP ME POR FAVOR
I'm rlly bad at this kind of math please help and write how you did each question

Answers

Answer:

its to blurry , sorry cant give you answer , too blurry. Make it less blurry ty3n i can answer it

If you make it less blurry I can answer it

-6+[tex]\frac{x}{4}\\[/tex]=-5

Answers

Add 6 to -5 which is 1, so you get

x/4 = 1

Multiply 4 and 1

The answer would be: x = 4
The answer is going to be x=4 have a great day ! Goodluck with your assignment :)

The cell phone company allows all users 450 text messages a month. Any text messages over the allowed amount are charged $0.25 per message. Craig only has $26 extra to sped on his cell phone bill. how many messages can he go over the allowed amount for the month without breaking his budget of $26? Let p represent the amount of text messages Craig can go over.
Inequality: ___________
Craig can send and receive ______________ extra text messages without breaking his budget of $26

Answers

Let's first find the total cost of the text messages Craig can send in a month. Craig is allowed to send 450 text messages without any additional charges. If he sends more than that, he will be charged $0.25 per message. Let's say he sends x additional messages over the 450 allowed:

Cost of additional messages = $0.25 * x

So, the total cost of Craig's text messages in a month is:

Total cost = Cost of allowed messages + Cost of additional messages

Total cost = $0 + $0.25x

Total cost = $0.25x

We know that Craig has a budget of $26 for his cell phone bill. We can set up an equation to represent this:

Total cost ≤ $26

Substituting the expression for the total cost of Craig's text messages, we get:

$0.25x ≤ $26

Dividing both sides by $0.25:

x ≤ 104

Therefore, Craig can go over the allowed amount by at most 104 text messages without breaking his budget of $26.

Answer: he can go over by 104

Step-by-step explanation:Total cost = $0 + $0.25x

Total cost = $0.25x

Total cost ≤ $26

Substituting the expression for the total cost of Craig's text messages, we get:

$0.25x ≤ $26

Dividing both sides by $0.25:

x ≤ 104

Therefore, Craig can go over the allowed amount by at most 104 text messages without breaking his budget of $26.

have a good day

Please help will give brainlest and special thanks

Answers

Answer:

To find the x-intercept, substitute in

0 for y

and solve for x. To find the y-intercept, substitute in

0 for x

and solve for y.

x-intercept(s): (−5,0)

y-intercept(s): (0,10)

Step-by-step explanation:

90 30 + 50 +(2x+10)=90

90 i hope is the answer <3

I NEED A GOOD GRADE SO I CAN BE A STEPPER NEXT YEAR !!!!!

Answers

The correct answer is 5

Answer: It's 7

Step-by-step explanation: Since all the sides are the same and it says JK is 7 inches HL must also be 7 inches.

Hope It helped!

Jill can make 50 flash cards every 20 minutes COMPLETE THE TABLE USING EQUIVALENT RATIOS.
MINUTES NUMBER OF CARDS
50
30
20 -----
-----
36

Answers

Answer:

minutes   :     # of cards made

20                             50

40                             100

60                             150

80                             200

100                            250

120                            300

140                            350

160                            400

180                            450

200                           500

220                           550

240                           600

260                           650

280                           700

300                           750

320                           800

340                           850

360                           900

380                           950

400                           1000

And please let me know if this helps.

What is the scale factor from the large triangle to the small triangle?

A. 1/2
B. 2/3
C. 1/3
D. 3/4

Answers

The Answer is: C = 1/3
The answer is C. 1/3. i took the test

Open this doc 2 (less blurry one!)

Answers

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x+16\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{1} \implies -3}}[/tex]

so we're really looking for the equation of a line whose slope is -3 and it passes through (-9 , 13)

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{13})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-9)}) \implies y -13 = - 3 ( x +9) \\\\\\ y-13-3x-27\implies {\Large \begin{array}{llll} y=-3x-14 \end{array}}[/tex]

Answer:

m = 1/3

m⊥ = -3

x1 = -9

y1 = 13

point slope: y-13 = -3(x+9)

slope intercept: y= -3x-14

Step-by-step explanation:

Equation given is in y=mx+b form, so I think m=1/3 (or whatever is right before the x cause it is little hard to see)

To find a perpendicular slope, you use the negative reciprocal of the given slope, so the perpendicular slope would be m=-3

x1 and y1 would be the given coordinates so -9 and 13 respectively

Finally plug in all this info into point slope form equation (y-y1 = m(x-x1)

Point slope would be: y-13 = -3(x+9)

Slope intercept would be: y= -3x-14

Hope this helps!

What is the range?
89 86 93 86 85 87

Answers

I think the range is the difference between the largest number and the smallest number.
So 93-85= 8

Answer: 8 (i think)

(so sorry if i’m wrong!!)
To find range you need to subtract the largest value from the smallest value. 93-85 is 8

....................

Answers

Answer: 350

Step-by-step explanation:

Divide it by the centimeter

Answer:

350  (*^▽^*)

Step-by-step explanation:

Can someone answer this question for me? asap please

Answers

Answer:

a) If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.

b) If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.

c) If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².

Step-by-step explanation:

a) To solve, set up a proportion. Volume is three-dimensional, so we need to cube.

(7/8)³=1029/x

Now we can solve using cross products to get 1536.

If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.

b) To solve the second one, we also set up a proportion. Height is one-dimensional, so we will not need exponents here.

7/8=14/x

Solve using cross products to get 16.

If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.

c) Now we are solving for area, which is two-dimensional. Therefore, we will need to square.

7/8²=392/x

Solve using cross products to get 512.

If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².

Hope this helps and good luck on your homework! For additional resources, check out The Maths Prof: Similarity parts 1-3.

Use the table to determine the relationship between feet and inches.

Feet Inches
1 12
2 ?
3 ?
4 ?

Which of the following graphs matches the relationship shown in the table?

A. Y
B. W
C. Z
D. X

Answers

Answer: Y

Step-by-step explanation: because 1 x 12 is 12 and 2 x 12 is 24

The answer to this question is A. Y

Can someone help please I'm in a hurry

Answers

you can make 48 batches of cupcakes
the best answer is 48 cookies

PLSSSS HELLP MEEEE This is confusing to me and I am not good at this

Answers

Answer:  21.4 pounds

Step-by-step explanation:

To calculate the amount of weight that is made up of body fat, you need to multiply the weight by the body fat percentage.

Weight of body fat = 162 pounds x 13.2% = 21.384 pounds

Then, round it to the nearest tenth which is,  21.4

Therefore, approximately 21.4 pounds of the individual's weight is made up of body fat.

Answer: 21.4 lb

Step-by-step explanation:

The question is asking how much weight consists of body fat.

We know that 13.2% of the total weight is body fat, and the total weight is 162 pounds.

Multiply to find out the body fat weight.

Percentage as a decimal over 1 * 162

0.132 * 162 = 21.384 lb

Round to nearest tenth: 21.4 lb

The equation shown describes a relationship between x and y.
y = 5x + 2
If the value of x increases by 1, what is the corresponding increase in the value of y?

Answers

y should increase by five every time

5x is just a multiple 5 but without knowing how many tines your multiplying. Now we know that x increases by 1 each time, so it should just be normal multiplying. 5(1) = 5, 5(2) = 10, 5(3) = 15 and so on. It's a constant increase of 5.

y is gonna increase by 5 every time so it’s 5(2), 5(3), 5(4) and so on

Anyone knows the answer???

Answers

Answer:b

Step-by-step explanation:

Answer:

#3 points are
(-4, 2)
(4, 2)

(-4, -2)

(4, 0)

#4 scale factor = 1/4

#5 scale factor = 1/2

Step-by-step explanation:

#3

take the given points and multiply the x and y by 2/3

#4 take any point and compare it to a similar point on the dilated graph. for example, you take a point from the original graph (-2, 4) and a point from the dilated graph (-1/2, 1) since you multiply -2 by 1/4 to get -1/2, that is your scale factor.

#5 same as #4 but with different points

Please help will give brainlest and special thanks

Answers

The answer is 30 because 80+10=90 and do you need to find out what times 3 equals 90 cause 90+90=180 and 3x30 is 90

Answer:

30

Step-by-step explanation:

3x+ 10= 100

-10           -10

3x=90

divide both sides by 3 nd you get 30

PLEASE HELP IM BEGGING
what is the estimate of the figure below

Answers

24 inches length x with

A store marks up their items by 30% to get the retail price. the store bought a bowl for $17. What is the retail price?

Answers

Answer:324

Step-by-step explanation:

ifdosfsf

Answer:

The retail price is $17 × 1.3 = $22.10.

Can someone help?? Thanks

Answers

Answer:17.6

Step-by-step explanation:

If 60% was taken off then what woold be left would be 40%. 40% translated into a decimal is 0.4 if you multiply that by 44 you would get the answer of 17.6.

Answer: $17.6

Step-by-step explanation:

100%-60%=40%. 40/100=0.4 and then you multiply 0.4x44=17.6. The price is now $17.6

What is the mode?
3 9 4 7 4 3 7 4 4 4

Answers

Answer:

it's 4

Step-by-step explanation:

4 appears more times than any number here

PLS HELP I NEED THIS NOW PLSSSSSSSSSSSSSSSSS
What does the symbol indicated by the arrows most likely represent?

a hurricane
low pressure
high pressure
high temperatures
this is sience ok

Answers

Answer:

Step-by-step explanation:

What does the symbol indicated by the arrows most likely represent?

high pressure there’s no picture.

It should be Low Pressure if I’m wrong I’m am very sorry

Help with number 4 please

Answers

Reflect 6 unit down and 3 to the right
6 unit down and 3 to the right sorry if I’m wrong

A sandwich store charges $21 to have 3 turkey subs delivered and $27 to have 4 delivered. a. Is the relationship between number of turkey subs delivered and amount charged proportional? Explain how you know. b. How much does the store charge for 1 additional turkey sub? c. Describe a rule for determining how much the store charges based on the number of turkey subs delivered.

Answers

The answer is also known ask 10
A. I don’t know . B. The store charges $6 for 1 additional turkey sub. C. A sub turkey is delivered for $7 . As 21/3 = 7 and u pay $21 for 3 sub turkeys . Every time it’s 3 it will be divisible by 21 . Example is it is 5 sub turkeys it will be $33 but if it is 6 sub turkeys it will be $42 .

help pls will give brainliest

Answers

Answer:

s = 7

Concept Used:

Linear pair axiom

Step-by-step explanation:

(6s-8) + 90 + 8s = 180 (Linear pair axiom)

14s = 98

s = 7

Answer:

7

Step-by-step explanation:

The 3 angles are on a straight line, meaning the angle is 180°.

We know that one angle is 6s-8°, another is 8s°, and the middle angle is 90° because of the small box.

We can set up an equation to find s:

6s-8+8s+90=180

simplify

14s+82=180

subtract 82 from both sides

14s=98

divide both sides by 14

s=7

Hope this helps :)

Help me please. Thanks in advanced

Answers

Answer:

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees. Therefore, we can set up an equation using the measures of the angles in triangle ABC:

ZABD + CBD + ABC = 180

Substituting in the given measures, we get:

(0.12x + 64) + (0.13x + 28) + ABC = 180

Simplifying and solving for x, we get:

0.25x + 92 + ABC = 180

ABC = 180 - 0.25x - 92

ABC = 88 - 0.25x

We know that the measure of angle ABC is 0.11x + 12. Substituting this into the equation for ABC, we get:

0.11x + 12 = 88 - 0.25x

Solving for x, we get:

0.36x = 76

x = 211.11

Therefore, the value of x is approximately 211.11.

Answer:

x = 352

Step-by-step explanation:

From the given Linear Pair, we can observe that ∠ABD and ∠CBD form a Straight Angle which is 180°.

∠ABD = 0.12x + 64°

∠CBD = 0.13x + 28°

Now we can understand that ∠ABD + ∠CBD = ∠ABC (Linear Pair)

∠ABC = 180°

So, ∠ABD + ∠CBD = 180°

(0.12x + 64°) + (0.13x + 28°) = 180°

(0.12x + 0.13x) + (64° + 28°) = 180° (Distribution Property)

0.25x + 92° = 180°

0.25x = 180° - 92°

0.25x = 88°

x = 88/0.25

x = 352


Hope my answer helps you ✌️

Mark BRAINLIEST

Please answer asap (it's due tomorrow), Mrs. Carter is preparing materials for a craft project. She needs to cut 5 meters of ribbon into pieces that are 0.5 meter long. How many 0.5-meter pieces can she cut from 5 meters of ribbon? Please check your answer, show your work.

Answers

Mrs. Carter can cut 10 pieces of 0.5-meter-long ribbon from 5 meters of ribbon.

Here's how you can calculate it:

- Divide the length of the ribbon by the length of each piece: 5 ÷ 0.5 = 10.

- Therefore, Mrs. Carter can cut 10 pieces of 0.5-meter-long ribbon from 5 meters of ribbon.

Answer:

10 pieces

Step-by-step explanation:

You take the total (5 meters) and divide it by the length she needs (0.5 meters) to get 10

0.75(s+13)=
Please help!

Answers

Answer:0.75x+9.75

Step-by-step explanation:

First, you will have to distribute (multiply) the 0.75 to both the s and 13 inside the parenthesis which would get you 0.75x+9.75

0.75s+12.25=0
0.75s=-12.25
s=-16.33

need help ASAP, would appreciate the assistance very much.

Answers

Answer:

(Question 1)

What are Corresponding Angles?

A pair of angles formed by two parallel lines and a transversal are said to be the corresponding angles.

Corresponding angles are formed only when,

One of them is interior and the other is exteriorThey are on the same side of the transversal andThey are not at the same vertex

The pairs of Corresponding Angles in the given figure are —

∠1 and ∠3∠2 and ∠4∠5 and ∠7∠6 and ∠8

You can write any two of them because the question says to write any two Corresponding Angles.


(Question 2)

What are Alternate Interior Angles?

Alternate angles that lie in the interior region of both the lines are called alternate interior angles

Alternate Interior Angles are formed only when,

Each pair of alternate interior angles is equal.Each pair of co-interior angles is supplementary.

The pairs of Alternate Interior Angles in this given figure are —

∠2 and ∠7∠3 and ∠6

These are the only two pairs of Alternate Interior Angles.


(Question 3)

What are Alternate Exterior Angles?

Alternate angles that lie in the exterior region of both the lines are called alternate exterior angles

Alternate Exterior Angles are formed only when,

Both lie on the exterior side of the lines.They are placed on the opposite sides of the transversal.

The pairs of Alternate Exterior Angles in this given figure are —

∠1 and ∠8∠5 and ∠4

These are the only two pairs of Alternate Exterior Angles.


(Question 4)

In this given Figure, Line segment AB is parallel to Line segment CD.

∠1 = 154°   [Alternate Interior Angles]

∠2 = 180 - 154°   [Linear Pair]

     = 26°


(Question 5)

In this given Figure, Line segment AB is parallel to Line segment CD.

∠1 = 97°   [Corresponding Angles]

∠2 = 82°   [Corresponding Angles]

∠3 = 180 - 97°   [Linear Pair]

    = 83°

Hope my answer helps you ✌️

Mark BRAINLIEST

Manuela spins a spinner with four equal sections, labeled A, B, C, and D, twice. If letter B is spun at least once, she wins. Otherwise, Gabriela wins. Which shows the winning sample space for Manuela?

Answers

Answer:

B

Step-by-step explanation:

is b because its that and I did the assiment

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Similar premonitions ran through the signal events of early American political history.Lincoln firmly took his stand in defense of the transcendent2 ideal of the Union as the sine qua non3 for the success of the American experiment in republican government. Indeed, as the conflict wore on, he spoke more and more frequently not just of the Union but of the nation. When he did speak of the Union, he presented it not as a means to an end but as an end in itself, something worthy of sacrifice in its own right. Lincoln well understood that the future of constitutional liberty, and the most worthy social reforms, depended in a fundamental way upon a strong and cohesive nation. Select the correct answer.Which is the best inference about Lincolns interpretation of his primary presidential duty? 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