Mathematics High School

The point (2, 1) is a solution to which of the following systems of equations?

2x + y = 5 and −2x + y = 2
−2x − y = −5 and 2x − y = 2
−x + y = 3 and −3x + y = −5
x + y = 3 and 3x − y = 5

Answers

Answer 1

[tex]\huge\boxed{\left \{ {{x+y=3} \atop {3x-y=5}} \right.}[/tex]

We can solve this problem by testing the solution against each system of equations. We'll do this by substituting the point into each equation for each system.

System 1 - [tex]\Large\textbf{X}[/tex]

[tex]\begin{array}{c|c}\textbf{First Equation}&\textbf{Second Equation}\\\cline{1-2}\begin{aligned}2x+y&=5\\2(2)+1&=5\\4+1&=5\\5&=5\\&\checkmark\end{aligned}&\begin{aligned}-2x+y&=2\\-2(2)+1&=2\\-4+1&=2\\-3&=2\\&\text{X}\end{aligned}\end{array}[/tex]

System 2 - [tex]\Large\textbf{X}[/tex]

[tex]\begin{array}{c|c}\textbf{First Equation}&\textbf{Second Equation}\\\cline{1-2}\begin{aligned}-2x-y&=-5\\-2(2)-1&=-5\\-4-1&=-5\\-5&=-5\\&\checkmark\end{aligned}&\begin{aligned}2x-y&=2\\2(2)-1&=2\\4-1&=2\\3&=2\\&\text{X}\end{aligned}\end{array}[/tex]

System 3 - [tex]\Large\textbf{X}[/tex]

[tex]\begin{array}{c|c}\textbf{First Equation}&\textbf{Second Equation}\\\cline{1-2}\begin{aligned}-x+y&=3\\-2+1&=3\\-1&=3\\&\text{X}\end{aligned}&\begin{aligned}-3x+y&=-5\\-3(2)+1&=-5\\-6+1&=-5\\-5&=-5\\&\checkmark\end{aligned}\end{array}[/tex]

System 4 - [tex]\Large\checkmark[/tex]

[tex]\begin{array}{c|c}\textbf{First Equation}&\textbf{Second Equation}\\\cline{1-2}\begin{aligned}x+y&=3\\2+1&=3\\3&=3\\&\checkmark\end{aligned}&\begin{aligned}3x-y&=5\\3(2)-1&=5\\6-1&=5\\5&=5\\&\checkmark\end{aligned}\end{array}[/tex]

Since both equations in the final system are true when solved with [tex](2, 1)[/tex], the answer is the last system.

Related Questions

PLZ PLZ PLZ HELP ME!!!!! I know this is alot to ask for but i need help. Im doing this test in math and i don't wnat to fail. PLZ PLZ PLZ HELP ME. Oh and #10 has a typo it is swimming 10ft. the question doesnt has 10ft on it. PLZ HELP ME​

Answers

Answer:

1). 14-22

if you take 22 away from fourteen, you get negative what? Its pretty simple it’s just subtraction. 11). Mark has NEGATIVE 5. Maria has POSITIVE 2. The positive number will always be greater than the negative number.

Let me know if you need additional help :)

11=x-(-20) do not know how to solve trynna get grade up​

Answers

Answer:

11/20 ; 0.55

Step-by-step explanation:

11= 20x

20x= 11

x= 11/20 ; 0.55

Answer:

x = −9

Step-by-step explanation:

Step 1: Simplify both sides of the equation

11 = x + 20

Step 2: Flip the equation

x + 20 = 11

Step 3: Subtract 20 from both sides

x + 20 − 20 = 11 − 20

x = −9

hi ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answers

Heyyyyyyytttttyyyyyyyy

The population of fish in a take was approximately 5.4 * 10 ^ 4 in 2012. The next year, 2013population tripled What was the opproximate population of fish in this in 2013?

Pleaseeee

Answers

5,4* 10^4 = 54000in 2012.
2013 = 54000*3 = 5,4*3* 10^4 = 162000 fishes. 1,62 *10^ 5

The population of fish in a lake was approximately 5.4 * 10 ^ 4 in 2012.

The approximate population of fish in this in 2013 since the amount of the fish tripled is 1.62 × 10⁵

Scientific notation is the proper format of denoting and representing large numbers into simpler forms multiplied by raising them to the power of 10.

Given that:

The approximate number of fish in 2012 is: 5.4 × 10⁴

In 2013, when the population of the fish tripled the amount it was in 2012;

Then, we can calculate the total population of fish in 2013 as:

[tex]\mathbf{=( 5.4 \times 10^4) \times 3}[/tex]

= 162000

= 1.62 × 10⁵

Therefore, we can conclude that the approximate population of fish in 2013 is: 1.62 × 10⁵

Learn more about scientific notation:

https://brainly.com/question/1705769?referrer=searchResults

Use the coordinates J(7, 8), K(1, 2) and L(5, 2) for AJKL.
The centroid for AJKL is at point M. What is JM rounded to the nearest tenth?
A.)2.4
B.) 4.3
C.) 4.8
D.) 7.2

Answers

Answer:

4.3

Step-by-step explanation:

What is an equivalent fraction to 10/20?

Answers

Answer:

1/2

Step-by-step explanation:

40 ÷ 1+ 3 - ( 3 × 7) + 7 - 5

Answers

Answer:

24

Step-by-step explanation:

Janice bought 28 apps for her phone that, altogether, used 1,348 MB of space. If half of the apps were free and the other half were $1.99 each, about how much money did she spend?

Answers

Answer: $ 27.86

28÷2=14

14×1.99= 27.86

I hope this is good enough:

Answer:

$28

Step-by-step explanation:

1,348/28

1,200/30

Each app used about 40 MB memory.

28/2= 14 apps

14*1.99=

14*2

=28

She spent about $28.

Traci collects donations for a dance marathon. One group of sponsors will donate a total of $6 for each hour she dances. Another group of sponsors will donate $75 no matter how long she dances. What number of hours, to the nearest minute, should Traci dance if she wants to raise at least $1,000?

Answers

Answer:155 hours

Step-by-step explanation:

$75+$6h=$1,000

Subtract $75 on both sides:

$75-$75+$6h=$1,000

$6h=$925

Divide 6 on both sides:

6/6h=925/6

h=154.1666667

After I rounded it and it was 155 hours

Solve the inequality.
2(4x-3) 2-3(3x) + 5X?

Answers

the second one

hope ya understand

Answer:

x[tex]\geq[/tex]0.5

Step-by-step explanation:

PLEASE PLEASE PLEASE HELP ME PLEASE!!

Answers

Answer:

x=14 to make the pay equal.

Step-by-step explanation:

Okay so what I did here is kind of time-consuming and I'm sure there's a better way, but I used a calculator to substitute a lot of different numbers into the equation to make it equal, and when I got to 14, the equations both ended up as 625.

the first one TO GET IT CORRECT will get brainliest plus 11 points :)

Answers

Answer:

6 x 2.5 = 15

8 x 2.5 = 20

L x W = 300 square units

Step-by-step explanation:

Brainliest?

In order to train for a marathon, Janelle researches training programs. One training program suggests running 396 miles over a period of 22 weeks. What is the average number of miles Janelle will run each week in this program?

Answers

Answer:

18 miles per week

Step-by-step explanation:

396/22 is 18miles/week

Does 3x-2=2x-3have infinitely many solutions

Answers

Hi there! :)

[tex]\large\boxed{\text{One solution: x = -1}}[/tex]

3x - 2 = 2x - 3

Subtract 2x from both sides:

3x - 2x - 2 = 2x - 2x - 3

x - 2 = - 3

Add 2 to both sides:

x - 2 + 2 = -3 + 2

x = -1

Therefore, the equation only has ONE solution.

Pedro is getting balloons for his grandfather's birthday party. He wants each balloon string to be 6 feet long. At the party store, string is sold by the yard. If Pedro wants to get 46 balloons, how many yards of string will he need?

Answers

Answer:

276

Step-by-step explanation:

7. Is y = x - 4 a linear function?

Answers

Answer:

yes it is cause it has a slope and stuff

Answer:

yes

Step-by-step explanation:


14x3 + 6x2 + 12xy2 =


Answers

Answer:

2x⋅(7x2−3x+6y 2 )

Step-by-step explanation:

x - 4y = 28
x+2y = -2
it’s substitution

Answers

Step-by-step explanation:

hope this will help you!!!.. plz follow me!!

❗️❗️❗️Solve❗️❗️❗️

6(x^2)-2x-4

Answers

Answer:

x=-1

Step-by-step explanation:

BRAINLIEST + FRIEND IF U ANSWER MY QUESTION!!!

Answers

Answer:

Sam Houston

Step-by-step explanation:

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

I think it's D. Sam Houston

Step-by-step explanation:

please help asap, will mark brainliest

Answers

Answer:

The answer is 122.07 if you round it, but the full decimal is 122.065556157

What is the solution to the following system??
A) (2.5,0)
B) (5,1)
C) (0,2)
D) (1,5)​

Answers

Answer:

C

Step-by-step explanation:

at least i think so

In a survey of 2,700 people who owned a certain type of​ car, 1,755 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

65%

Step-by-step explanation:

survey of 2,700 people who owned a certain type of​ car, 1,755 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Total car number of car owner= 2,700

Then the percentage that satisfied is

1,755

1755/2700*100= 65%

What is the area of the figure down below

Answers


68


Explanation:

So to get this answer you need to split it into smaller shapes. We already have the squares so we know that 3*3 is 9 and then we double that because there are two of them.

So, so far we have 18+x

We need to take the middle shape and split it into two trapezoids.

The area for trapezoids is T=(a+b/2)h

So T= (3+7/2)5
T= 5*5=25
And then we would double that because there are two of them so 50 and then fill it in for x
18+50= 68 is the area of the figure.

Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.

Answers

Answer:

9

Step-by-step explanation:


Find the equation of OP.
F (x + 4)2 + (y – 2)2 = 3
G (x + 4)2 + (y - 2)2 = 9
H (x – 4)2 + (y + 2)2 = 3
J (x - 4)2 + (y + 2)2 = 9

Answers

Answer:

G

Step-by-step explanation:

what percentage of students earned A’s on their paper ?

Answers

Answer:

21% or C

Step-by-step explanation:

If 60 students either didn't pass, got Cs or Bs, then 16 out of the 76 got As which is 21 percent.

Please help me I don't understand the equation​

Answers

Answer:

0.00284090909

Step-by-step explanation:

It’s basicly a unit conversion that converse whatever you have to miles/h, so you are getting a miles and get a time and do the math, the final answer will be 180/(5280*12)=0.00284090909

This package of sliced cheese costs $2.97. How much would a package with 18 slices cost at the same price per slice?

Answers

$53.46 would be the cost of a package with 18 slices of cheese! Hope this helped! Mark if correct!

Answer:

$53.46

Step-by-step explanation:

The answer is 53.46 because 2.97 multiplied by 18 is 53.46

Pls help me this is due tmr morning

Answers

the answer is y = 3x - 6
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