How can you determine the number of solutions of a system of linear equations by inspecting its equations?

Answers

Answer 1

Step-by-step explanation:

To find - How can you determine the number of solutions of a system

              of linear equations by inspecting its equations?

Proof -

There exists three types of solution for a system of linear equations.

1. No solution.

2. Unique solution.

3. Infinite many solutions.

Now,

Let the 2 linear equations are as follows :

y = ax + b

y = cx + d

1. For no solution -

a = c and b ≠d

For example-

y = -2x + 5

y = -2x  - 1

Subtract first equation from second , we get

y - y = -2x - 1 - ( -2x + 5)

⇒0 = -2x - 1 + 2x - 5

⇒0 = -6

Not possible

So, There exist no solution.

2. For unique solution -

a ≠ c and b , d can be any value

For example -

If b and d are same ,

y = 2x - 4

y = -3x - 4

Subtract equation 1st from 2nd , we get

y - y = -3x - 4 - ( 2x - 4)

⇒0 = -3x - 4 - 2x + 4

⇒0 = -5x

⇒x = 0

⇒y = 2(0) - 4 = -4

∴ we get

x = 0, y = -4

If b and d are different

y = 2x - 4

y = -3x + 5

Subtract equation 1st from second

y - y = -3x + 5 - 2x + 4

⇒0 = -5x + 9

⇒-5x = -9

⇒x = [tex]\frac{9}{5}[/tex]

⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]

∴ we get

x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]

3. Infinitely many solution -

a = c and b = d

For example -

y = -4x + 1

y = -4x + 1

Subtract equation first from equation second

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

⇒0 = -4x + 1 + 4x - 1

⇒0 = 0

Satisfied

So, Infinite many solution possible.


Related Questions

Find the area of a circle with radius, r = 7.49m. Give your answer rounded to 2 DP.

Answers

Answer:

Area ≈ 176.24m²

Hope it helps

Please mark me as the brainliest

Thank you

If u can solve 6 word problems in 5 minutes how many could you solve per minute?

Answers

Answer:

You can solve 1.2 word problems per minutes

Step-by-step explanation:

If 6 word problems were solved in 5 minutes, you must put this into a fraction. We're looking for how many word problems could be solved per minute, so we divide 5 by itself to get 1 and whatever you do to the bottom, you must do to the top, so 6 divided by 5 is 1.2

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Answer:

So, the answer is 7 y

Step-by-step explanation:

Both arrows are pointing toward the 7 and it is in y! I have been in 12 grade already so dont worry :)

What is the length of the unknown side?

Answers

Answer:

use Pythagoras theorem

✓12x12+16x16

✓400

20

Answer:

20

Step-by-step explanation:

Hope this helped!

Question
2
1 pts
José invested $3000 in a 5 yr GIC that paid 3.95%/yr, compounded annually.

Answers

Answer:

this doesn't make any sense

Step-by-step explanation:

What is the solution to the inequality-6(p-8)<-12

Answers

Answer:

p < 10

Step-by-step explanation:

-6 (p - 8) < -12

-6p + 48 < -12

- 48 -48

-6p < -60

/-6 /-6

p < 10

YO SOMEBODY HELP PLS IM STUCK

Answers

Answer:

x > 1

Step-by-step explanation:

subtract 6 from both sides

Divide both sides by 2

brainliest for the fastest answer!!!!!!!!
its super easy

Answers

Answer:

The answer is B number os shoes ihope it help

Percy has $50 in a savings account. The interest rate is 10% per year and is not compounded. How much will he have in 1 year?

Answers

Answer:

Step-by-step explanation:

Take the 50 and multiply by 1.1 (this is 10% if you dont want to go .1 and add that to 50)

50*1.1=x

50*1.1=55

There will be a total of 55 Dollars in the savings account. He has earned 5 dollars in interest.

Hope This helps :)

Answer:

70

Step-by-step explanation:

just doubled

Need this done in 5 minutes

Answers

Step-by-step explanation:

40, 58, 58, 72, 74, 74, 76, 81,  83, 84, 92

1      2    3   4        5     6      5     4   3    2   1

1) A. 74

2) B. 40

3) A. 92

4) A. 58

Brainlist pls!

due tomorrow i need help

Answers

Two figures are similar if they have the same shape but not necessarily the same size. The figures below are NOT congruent.

Ben takes a 45 minute test. After answering 10 questions, the timer indicates that one-fifth of the total time is up. How much time did Ben take to answer the 10 questions *

Answers

it took Ben 9 minutes to answer 10 questions

Shrings dining room table is round and has a radius of 4.5 feet. What is the tabletops area? Plz

Answers

Answer:

The answer should be 63.63! you might need to round it to 63.6 or 64

Step-by-step explanation:

Which expression is equivalent to 12x + 20y?

Answers

15x+20y+5z I’m pretty sure

A(b) is a function.


. A(b)
A. True
B. False

Answers

Answer:

B

Step-by-step explanation:

NOTE:

it might be wrong since im in geometry, not algebra, i used to know this

https://wfs.fireflycloud.net/resource.aspx?id=677205

Answers

Answer:

huh????????????????.??????

?? whatt i dont get it lol

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Answers

Answer:

I really dont know

Step-by-step explanation:

the explination is i

Type the correct answer in each box. Use numerals instead of words. Bethany collected 200 survey responses regarding recycling behaviors in her city. Of those responses, 174 people responded that they participate in the city’s recycling program. Use this information to complete the statement. Round all answers to the nearest hundredth. The approximate sample proportion is , which means that % of the people surveyed do not participate in the city’s recycling program.

Answers

Answer:

13% did not participate in citys recycling program not sure about the first part

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation shown has an unknown number.
Blank divided by 3/7 = 7/15
Enter a fraction that makes the equation true

Answers

Answer:

45/49

Step-by-step explanation:

1. Find the value of the variable x.

A) 7 √2/2
B) 7 √3/2
C) 14 √3
D) 14/3

Answers

Answer:

[tex] \frac{ \sqrt{7} }{2} [/tex]

Step-by-step explanation:

The triangle is an isosceles triangle. Because the triangle is an isosceles triangle, the height and base of the triangle are equal to eachother.

a² + b² = c²

right now we have c² which is 7

a² + b² = 7

[tex] \frac{ \sqrt{7} }{2} [/tex]

because a² and b² are = to eachother

now im lost dony listen to me lol.

Write 4/5 as a decimal

Answers

Answer:

4.5 : i think thats the answer i don't know

Answer:
4/5 as a decimal is 0.8
Hope this helps! Have a great day :)

For every 2 apples in kail's orchard,there are 4 pears. In sam's orchard , there are 10 pears for every 5 apple. If the number of pears in proportional to the number of apples, What is constant proportionality

Answers

Answer:

2/5

Step-by-step explanation:

cause u divied

9. A 16-ft ladder is leaning against the side of a house. The ladder touches the ground 9 ft away from the house. What angle does the ladder make with the ground?
Round to the nearest WHOLE number.
Note: this is a trigonometry question

Answers

Answer:

Check pdf

Step-by-step explanation:

55.77°

EXPLANATION:

In ◣ ABC, (consider the diagram)

cosΦ = b/h = 9/16

cosΦ = 9/16

Φ = 9/16 × cos-¹

Φ = 55.77

Hence, the angle between the ladder and ground is approximately 56°.

Can someone help and give me a step by step explanation please?!

Answers

9514 1404 393

Answer:

∠QSR = 78°∠SQR = 51°

Step-by-step explanation:

The measure of an inscribed angle (QTR) is half the measure of the arc it intercepts. The measure of an arc is the same as the measure of the central angle it intercepts. So, we have ...

  ∠QSR = 2×∠QTR

  ∠QSR = 2×39°

  ∠QSR = 78°

__

Sides SQ and SR are radii of circle S, so are the same length. That means triangle QRS is an isosceles triangle and the base angles SQR and SRQ are congruent. The sum of angles in a triangle is 180°, so we have ...

  ∠QSR + 2(∠SQR) = 180°

  78° + 2(∠SQR) = 180° . . . . fill in the value we know

  2(∠SQR) = 102° . . . . . . . . . subtract 78°

  ∠SQR = 51° . . . . . . . . . . . . .divide by 2

PLEASE HELP ASAP I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER

Find the values of x, y and z.

Answers

Answer:

X = 53 degrees

Y = 74 degrees

Z = 53 degrees

Step-by-step explanation:

So if you knew that all angles in triangles add up to 180 degrees. You first want to find Y. 180 - 36 - 70 is equal to 74. So, Angle Y is 74 degrees. Line XYZ is a line that has a 180 degree on there. So 180 - 74 and divide that by 2 to find X and Z. 180 - 74 is 106. 106/2 = 53. Therefore, X and Z are 53 degrees, Y is 74 degrees.

Y =74

Step-by-step explanation:

Add the number till u get 180

Use synthetic division to solve

Answers

(9+32)r+21
—————
r+3

41r+21
————
r+3

Hope this helps
r+3333333333333333333333333333333

1. In triangle ABC, the measure of ∠ABC is 42°, and the measure of ∠BCA is 113º.
What is the measure of ∠CAB?

How do you know that is the answer?

Answers

Answer:

if I am correct it would be 25 degrees. hope this helps!

Step-by-step explanation:

Please help me i need to pass math class
Simplify each expression.
1. (-6p - 8) - (2p - 6)
2. (-8r - 2) + (4r - 3)
3. (-z - 8) - (6z - 5)
4. (-s - 5) + (-2s + 2)
5. (-7s + 4) - (-8s + 4)
6. (-4f + 9) - (8f + 9)
7. (-8f) + (-f + 8)
8. (4p - 4) + (-7p - 7)
9. (7v - 9) - (6v + 9)
10. (-3g) + (5g - 5)

Answers

1. -8p-2 the rest is to much

HELP ME PLS NOW I NEED YOU PPLS BRAINS

Answers

Since it has a line under > that means it equal to 7 and x is bigger than 7 so 8, 9, 10... so right
The second answer

Answer:

C and D

Step-by-step explanation:

I went to a website (https://mathbitsnotebook.com/JuniorMath/Equations/IQBasicInequalities.htm) and double-checked what the correct answers were. I apologize for the hassle I may have caused you.

Find the percent of increase from 36 inches to 43 inches. Round to the nearest tenth of a percent if necessary.

Answers

Answer:

27.78

Step-by-step explanation:

(46-36):36*100 =

(46:36-1)*100 =

127.77777777778-100 = 27.78

Now we have: What is the percentage increase/decrease from 36 to 46 = 27.78

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