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.


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I really dont know

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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.

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Answer:

use Pythagoras theorem

✓12x12+16x16

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20

Answer:

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Step-by-step explanation:

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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.

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Step-by-step explanation:

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Answers

Answer:

27.78

Step-by-step explanation:

(46-36):36*100 =

(46:36-1)*100 =

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Answers

Answer:

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

Answer:
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Hope this helps! Have a great day :)

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

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Answer:

70

Step-by-step explanation:

just doubled

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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

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Brainlist pls!

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:

1. Find the value of the variable x.

A) 7 √2/2
B) 7 √3/2
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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

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

because a² and b² are = to eachother

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Answer:

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Answers

Answer:

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Step-by-step explanation:

-6 (p - 8) < -12

-6p + 48 < -12

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Answers

Answer:

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Step-by-step explanation:

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Answers

it took Ben 9 minutes to answer 10 questions

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:

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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 ...

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__

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 ...

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

Answers

Answer:

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Step-by-step explanation:

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.
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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°.

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Answers

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A. True
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Answers

Answer:

B

Step-by-step explanation:

NOTE:

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Answers

(9+32)r+21
—————
r+3

41r+21
————
r+3

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r+3333333333333333333333333333333

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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