Which method would be best (quickest) for solving the system below:
3x - 4y = -2
y = 2x + 1

Answers

Answer 1
To solve with Elimination:

Write the equations under one another, like this:

2x - y = -1
+ 3x + 4y = 26

Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.

If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4. To do this, simply multiply the first equation by 4, this will create MAGIC!

4( 2x - y = -1)
+ 3x + 4y = 26

Be certain to Distribute across the entire first equation, so multiply all three terms by 4.

8x - 4y = -4
+ 3x + 4y = 26

Now add straight down (vertically). The y term will be eliminated.

11x = 22

Divide both sides of the equation by 11.

x = 2

Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.

3x + 4y = 26

3(2) + 4y = 26

6 + 4y = 26

Subtract 6 from both sides of the equation.

4y = 20

Divide both sides of the equation by 4.

y = 5

That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).

Related Questions

Pls help fast !! Thanks
Simplify the expression 4f × 2g + 3h

A. 8fg + 3h
B. 24fgh
C. 9fgh
D. 6gf + h

Answers

Answer:

A. 8fg + 3h

Step-by-step explanation:

[tex]4f × 2g + 3h \\ \\ = 4 \times 2 \times f \times g + 3h \\ \\ = 8fg + 3h[/tex]

Step-by-step explanation:

[tex]4f \times 2g + 3h \\ = (4 \times 2)fg + 3h \\ = 8fg + 3h \\ [/tex]

.FIND THE DIFFERENCE OF 8,328 AND 459?​

Answers

Answer:

7869

Step-by-step explanation:

   8,328

-     459

________

    7,869

7,869 is the answer


Subtraction

What is the Scale Factor?
Point B was dilated using C as the center of dilation
What is the scale factor?
Explain your thinking.

Answers

9514 1404 393

Answer:

5the length of the expanded segment is 5 times the original length

Step-by-step explanation:

We have to assume that the image of B is the large dot at upper right. We further have to assume that the distance between dots on the line segment is equal to CB.

The scale factor multiplies the distance from C. That distance has been multiplied by 5, so the scale factor is 5.

Please help, thank you.

The question is in the picture

Answers

Answer:

D

Is the answer okkkkkkkkkkkkkkkk

Answer: A regular decagon has all sides of equal length and each internal angle will always be equal to 144°.

Step-by-step explanation:

Please ASAP.
The rectangle on the right is a scaled copy of the rectangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.

Answers

You probably don’t need this anymore, but i think it’s 1.5

Scale factor is  [tex]\frac{14}{21}[/tex].

What is a scale factor?

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

Given

The rectangle on the right is a scaled copy of the rectangle on the left.

[tex]\frac{42}{63}[/tex] and 15 ÷ [tex]\frac{45}{2}[/tex]

[tex]\frac{42}{63}[/tex]

Rationalizing [tex]\frac{42}{63}[/tex] by 45

= [tex]\frac{42(45)}{63(45)}[/tex]

= [tex]\frac{1890}{2835}[/tex]

15 ÷ [tex]\frac{45}{2}[/tex]

Rationalizing 15 ÷ [tex]\frac{45}{2}[/tex] by 63

= [tex]\frac{30(63)}{45(63)}[/tex]

=  [tex]\frac{1890}{2835}[/tex]

If we want to find the scale factor we have to equal the proportions of two rectangles.

Scale factor =  [tex]\frac{1890}{2835}[/tex] = [tex]\frac{14}{21}[/tex]

Hence, scale factor is  [tex]\frac{14}{21}[/tex].

Find out more information about scale factor here

https://brainly.com/question/22312172

#SPJ2

joe finished his english assigments in 1/3 hours. Then he completed his chemistry assigment in 1/8 hours. What is the total amount of time joe spent doing these two assigments as a fraction in simplist form./ Aleks

Answers

To answer, we need to add the two fractions. However, to add them, they need to have a common denominator (the number on bottom). One easy way to do this is to multiply both so they are the same number. Use the opposite number! Then, you can add the numbers straight across. You will most likely need to simplify. If you have any further questions, let me know!
The lowest common denominator would be 24 for these 2 fractions...so change 1/3 into 8/24, and 1/8 into 3/24. Add them together and you see that it took him 11/24 hours to do both assignments. That won’t simplify any, so 11/24 should be your answer.

Can anyone help me with these 3 please !
I’ll mark you as a brainliest.

Answers

Answer:

72

270

600,000

I wasn't sure what this question means, but I did the math??

like are supposed to switch around the numbers..? haha...

Answer:

1. 72

2. 270

3. 600,000

hope this helps!!

Step-by-step explanation:

HELP!!! What mistake did I make? And what would u suggest to help me???

Answers

Answer:

All the dots need to be on the line, and maybe dont add so many dots

Step-by-step explanation:

You need to have an equal amount of dots on each side since it is a scatter line.

Hi I am really bad at math and need to know about fractions I HATE MATH I’m super nervous so ya if you know anything about fractions please help me!!! :)

Answers

Answer:

how to add and subtract fractions

Step-by-step explanation:

ok so we can start with adding so when you add fractions you can first start out by making the denominators the same number to make it easier so here is an example

7/9 + 3/10  you could make the denomonatiers the same or just do 9x10 and 7x10 + 3x9 and 10x9 and then if you multiply the numbers and added up all the sums you would get to fractions 70/90 + 27/90 so you add them up and science the denominators are the same you just leave them the same number so it would just be 70+27 so you would get 97/90 and because the denominator is 90 and we have 97 for the numerator 97 fits into 90 1 time with 7 left over   so the whole number would be 1 and then 7/90  

Step-by-step explanation:

Multiplying Fractions:

example: 2/3·2/3

multiply numerator=top number2·2=4 multiply denominator=bottom number3·3=9combine the terms..4 and 9=4/92/3·2/3=4/9

Dividing Fractions:

example: 2/3*2/3

reverse second fraction thats getting divided..2/3=3/2convert into multiply symbol.2/3·3/2multiply the like terms..2/3·3/2=6/6..2/3*2/3=1 whole..

Combine Fractions:

example:2/3+2/3

keep denominator and combine numerator only if denominator is the same..2+2=4combine the numerstor and denominator..4 and 3=4/32/3+2/3=1 1/3

Subtract Fractions:

example:2/3-2/3

keep denominator if similar..subtract numerator..2-2=0combine numerator and denominator..0 and 3=0/32/3-2/3=0

What would the area be for a circle with the diameter of 7

Answers

Answer:

The answer is 38.48

Step-by-step explanation:

Picture with explanation provided below.

HELP THIS IS DUE VERY SOONN

Answers

Answer:

A: 7

B: 84,035

Step-by-step explanation:

The population increases by 7 each time, so 12,005x7=84035.

(Side note: I'm not completely sure what the "exponential function" is but I think the answer is correct. Check over it yourself to be sure :)

Answer:

a.  x plus 5 times 7

b. 84035

Step-by-step explanation:

is anybody else just really tired rn???

Answers

Answer:

yep i am very tireddddfdf

Answer:

YEAAA I'm like super tired for no reason, even though I really didn't do anything today :/

It’s PreCal I just need a method to solve it

Answers

Answer:

see explanation

Step-by-step explanation:

Using the identities

tanx = [tex]\frac{sinx}{cosx}[/tex] , cotx = [tex]\frac{cosx}{sinx}[/tex]

Consider the left side

[tex]\frac{tanx}{tanx+cotx}[/tex]

= [tex]\frac{\frac{sinx}{cosx} }{\frac{sinx}{cosx}+\frac{cosx}{sinx} }[/tex]

= [tex]\frac{\frac{sinx}{cosx} }{\frac{sin^2x+cos^2x}{cosxsinx} }[/tex]

= [tex]\frac{\frac{sinx}{cosx} }{\frac{1}{cosxsinx} }[/tex]

= [tex]\frac{sinx}{cosx}[/tex] × [tex]\frac{cosxsinx}{1}[/tex] ← cancel cosx on numerator/ denominator

= sin²x

= right side

Sam had 225 grams of raisins. After buying another two bags of raisins he then had
175 grams of raisins
He writes this equation where r represents number of bags of raisins to describe how
225r+2=1475
Is he correct? Explain your answer.
How many grams of raisins were in one bag?

Answers

Answer: No, he is not correct, the correct equation is:

225 + 2*r = 1475

Solving that, we can find that each bag of raisins has 625 grams of raisins.

Step-by-step explanation:

I suppose that the problem is as follows:

"Sam had 225 grams of raisins. After buying another two bags of raisins he then had  1475 grams of raisins"

Then, if each bag of raisings has r grams of raisings, two bags will have two times that, or:

2*r grams of raisings.

Then if we take what he had at the beginning, and we add these 2*r grams, we should get the 1475 grams that he has at the end:

225 + 2*r = 1475

This is what he should get.

and we can solve it for r, to get:

2*r = 1475 - 225 = 1250

r = 1250/2 = 625

r = 625

This means that each bag of raisins has 625 grams of raisins.

But instead, he got:

225*r + 2 = 1475

In this case, he multiplied his previous amount of raisings by the amount that each bag has, so his equation is wrong.

Histograms in mathh
I need help with it because I am clueless!

Answers

Total number of squares = 60 + 80 + 110 + 115 + 95 + 40 = 500
1000/500 = 2 so each little square represents 2 people
60 x 2 as there’s 60 squares from 6-10 so answer is 120

Help please it’s a grade

Answers

For the right angle triangles to find the hypotenuse square both the sides that are given and add them together, then you need to square root your answer
If you are finding a different side like triangle 2 use a^2 = c^2 - b^2 where a is the side you are finding, c being the hypotenuse and b being the other side.

pls help.........with the help of pic​

Answers

Answer:

Her journey by car.

Step-by-step explanation:

3/5 is more than 3/10. I hope this helps :)

Answer:  3/10 of her journey by autorikshaw.

Step-by-step explanation:

Pls help tell me how to do it

Answers

(13 * 17) /2 = 110.5


Explanation: b * h / 2

The speed of a car in mph varies directly with the speed of a car in kph. The speed of 75
mph is equivalent to 120 kph. How many kph is 45 mph?

please help asap !

Answers

Answer:

72.42 kilometers per hour


Another chance for brainliest if it correct ! Please help

Answers

Answer:

A B and C are true

Step-by-step explanation:

A, B, and C are the correct answers

You look at the order of abc and xyz
A goes with x
B goes with y
C goes with z

Viasat has a $100 setup fee and costs $65 per month. Geo Satellite has a setup fee of $30 and costs $70 per month. Write a system of equations to represent this situation. In how many months will both providers cost the same? What will that cost be?​

Answers

Answer:

Step-by-step explanation:

I don’t know

Answ

i dont know

Step-by-step explanation:

please help me, I am so confused. Thanks​

Answers

Answer:

c. 80

Step-by-step explanation:

cos x = sin(x-70)

cos x = cos [90-(x-70)]

cos x = cos (90-x +70)

cos x = cos 160 -x

x= 160-x

2x = 160

x =80

In a bag there are blue sweets, red sweets and yellow sweets. The number of blue sweets is four times the number of yellow sweets. The number of red sweets is half the number of yellow sweets. Find the percentage of sweets in the bag that are yellow.

Answers

Answer:

18.18%

Step-by-step explanation:

The percentage of sweets in the bag that are yellow is as follows:

Let us assume the number of yellow sweets be x

So for number of blue sweets be 4x

And, the number of red sweets be 0.5x

So it could be written as

Blue Red Yellow

4        0.5    1

8        1        2

So for yellow, the percentage is

= 2 ÷ (8 + 1 + 2)

= 2 ÷ 11

= 18.18%

Middle school students were asked how they got to school each morning. There were 375 students who said they rode the bus. This number represents 60% of the school enrollment. How many students are enrolled?

Answers

Answer:

625 students

Step-by-step explanation:

if the simple answer interest on 2,000 for 10 years is 1,600, then what is the interest rate

Answers

Answer:

8%

Step-by-step explanation:

Solving our equation

r = 1600 / ( 2000 × 10 ) = 0.08

r = 0.08

converting r decimal to a percentage

R = 0.08 * 100 = 8%/year

The interest rate required to

accumulate simple interest of $ 1,600.00

from a principal of $ 2,000.00

over 10 years is 8% per year.

There are 32 students in the class. Of the class 3/8 of the students bring their own lunch. How many students bring their own lunch?

Answers

12 students because 32 times 3 is 96, dividing that by 8 would be 12

Would it be better to have a higher interest rate on a loan or on an investment? Explain.

Answers

Answer:

When a company borrows money it is better to have a low interest rate. The lower the interest rate, the less amount of money the company has to pay back as interest on the loan.

Step-by-step explanation:

Is it better to have a higher interest rate when a company borrows money or to have a lower interest rate?

PLEASE HELP ANSWER THIS ASAP!!! :)

Answers

Answer:

C, 42 degrees

Step-by-step explanation:

Considering  angle BAD is 60 degrees, that makes angle BCD also 60 degrees. Since parallelograms have 360 degrees in total, we're still missing 240 degrees. Since angles BAD and BCD are congruent (equal), that means that angles ABC and ADC also have to be congruent. To find their angles, we do 240 divided by 2, which equals 120. Now that we know all of the angles, lets focus on angle ADC. Since angle 1 has been given to us, all we need to do is subtract 78 from 120 which turns out to be 42 degrees, which is the answer.

2. Find the vector equations of the following lines:

a. A=(6,5,7),m=2i+5j–k
b. A=(8,6,2),B=(3,4,1)

Answers

Answer:

a) The vector equation

[tex]AB^{-} = -4i^{-} -0j^{-} -8k^{-}[/tex]

b) The vector equation

  [tex]AB^{-} = -5i^{-} -2j^{-} -k^{-}[/tex]

Step-by-step explanation:

Step(i):-

a)

Given that the points are A( 6,5,7) and B = m = 2i+5j-k

OA = 6i+5j+7k and OB = 2i+5j-k

AB = OB-OA

    =  2i+5j-k - (6i+5j+7k)

    = 2i -6i +5j-5j-k-7k

   =  [tex]-4i^{-} -0j^{-} -8k^{-}[/tex]

b)

Given that the points are A( 8,6,2) and B = (3,4,1)

OA = 8i+6j+2k and OB = 3i+4j+k

AB = OB-OA

     = 3i+4j+k -(8i+6j+2k)

    = 3i -8i +4j-6j+k-2k

    =  [tex]-5i^{-} -2j^{-} -k^{-}[/tex]

David’s salary used to be £19,500 before he received a 8% pay rise. Work out how much David is now paid?

Answers

Answer:

21060

Step-by-step explanation:

19500÷100=195

195×8=1560

1560+19500=21060

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