The system of equations below is consistents with infinity many solutions where a and b are constants.Find the values of a and b. 2x+y=6 ax+by=9

Answers

Answer 1

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.

Step-by-step explanation:

Two linear equations with two variables have infinite solution if and only if they are linearly dependent. That is, one linear equation is a multiple of the other one. Let be the following system of linear equations:

[tex]2\cdot x + y = 6[/tex] (1)

[tex]a\cdot x + b\cdot y = 9[/tex] (2)

The following condition must be observed:

[tex]r = \frac{a}{2} = \frac{b}{1} = \frac{9}{6}[/tex] (3)

After some quick operations, we find the following information:

[tex]r = \frac{3}{2}[/tex], [tex]a = 3[/tex], [tex]b = \frac{3}{2}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.

Related Questions

If y represents a student's age, which inequality shows that you must be older than 14 to
try out for the basketball team?
A y < 14
B. y > 14
c.y > 14
D. 14 = y

Answers

Answer:

B. y > 14

y which is students age is greater than 14

The radius of a circle is 7 millimeters. What is the circle's area?
Use 3.14 for a.
square millimeters

Answers

Answer:

153.86

Step-by-step explanation:

formula - πr²

= 3.14 * 7²

= 153.86

Can you plz help me!dddddddd

Answers

Answer:

We are finding hypotenuse:

6^2 + 8^2

36 + 64 = 100

Now we need to find a number that should be squared to equal 100.

10^2 = 100!

10 is your answer.

There are 4 second-grade classrooms that share 15 packs of paper. How much paper should each classroom get

Answers

Answer:

3.75

Step-by-step explanation:

How do you do this ??????????????????????

Answers

Answer:

Step-by-step explanation:

you can take the rectagel and you x the rectagel

Johann borrows money from his parents to purchase a bike. He makes weekly payments to his parents to repay the money
borrowed. The total amount of money repaid at the end of week n can be represented using the recursive formula a, = 10+ an-1-
At the end of the fourth week, Johann had repaid his parents a total of $55. What is the total amount Johann had repaid his
parents at the end of the first week?
o $10
$20
$25
$35

Answers

Answer:

$25

Step-by-step explanation:

An = 10 + An-1

At the end of 4th week ; amount repaid = $55

A4 = 10 +

An = a + (n - 1)d

n = 4

A4 = 10 + (4 - 1)d

55 = 10 + 3d

55 - 10 = 3d

45 = 3d

x=440

hope this helps,have a great day!!

~Pinky~

Jack wants to find out which can of pineapples is the best buy. He has a choice of four
different-sized cans. Which can has the lowest unit price per ounce?

A. 8 ounces for $1.44
B. 18 ounces for $2.88
C. 10 ounces for $1.62
D. 6 ounces for $1.14

HURRY PLEASE

Answers

18 ounces for 2.88

2.88 divided by 18 is .16 which is 16 cents per ounce which is the cheapest of all the options.

write the measure of each of the missing angle measures in the diagram above.

Answers

Answer:

<2= 65°

<3= 65°

<4= 115°

<5= 115°

<6= 65°

<7=65°

<8=115°

Pls help rationalize

Answers

Answer:

1= 0.109

2= 3.46

3 = -(minus)1.24

Step-by-step explanation:

Answer:

See answers below.

Step-by-step explanation:

All of these use the same idea: multiply numerator and denominator by the conjugate radical (an identical expression but with the sign between terms changed).

[tex]\frac{1}{13-\sqrt{15}}\cdot\frac{13+\sqrt{15}}{13+\sqrt{15}}=\frac{13+\sqrt{15}}{169-15}}\\\\=\frac{13+\sqrt{15}}{154}[/tex]

[tex]\frac{1}{\sqrt{13}-\sqrt{11}} \cdot \frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}+\sqrt{11}}=\frac{\sqrt{13}+\sqrt{11}}{13-11}\\\\=\frac{\sqrt{13}+\sqrt{11}}{2}[/tex]

[tex]\frac{1}{\sqrt{21}+\sqrt{29}}\cdot\frac{\sqrt{21}+\sqrt{29}}{\sqrt{21}+\sqrt{29}}=\frac{\sqrt{21}+\sqrt{29}}{21-29}\\\\=\frac{\sqrt{21}+\sqrt{29}}{-8}[/tex]

Note: Here's an example of what happens when you multiply conjugate radicals.

[tex](\sqrt{13}-\sqrt{11}})(\sqrt{13}+\sqrt{11})=13-\sqrt{11}\sqrt{13}+\sqrt{13}\sqrt{11}-11=13-11[/tex]

When you FOIL those binomials, the square roots go away!

How can I find the height of a pyramid that has a base of 13m and a 13m lateral height

Answers

Answer:

Dnnd

Step-by-step explanation:

Answer:

The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. A pyramid is a regular pyramid if its ... A triangular pyramid has a triangle base. regular pyramid. A right pyramid is ...

Missing

Step-by-step explanation:

If the circumference of a circle is 31.4 feet , What is the radius of the circle use 3.14 for π

Answers

Answer:

144

Step-by-step explanation:

a friend is buying flowers for mothers day. because it is a friends 38th birthday, your friend wants to have 38 of her favorite flowers. her favorite flowers are daisies at $1.50 each and tulips at $2.50 each. IF the total bill is $67 how many tulips were bought?

Answers

Answer: She bought 28 daises and 10 Tulips.

Step-by-step explanation:

Let x represent the number of daises bought.

Let y represent the number of tulips bought.

Your friend want to have 38 of her favorite flowers. This means that

x + y = 38

Her favorite flowers are daisies at 1.50 each and tulips at 2.50 each if the total bill was 67, it means that

1.5x + 2.5y = 67 - - - - - - - - - - - - 1

Substituting x = 38 - y into equation 1, it becomes

1.5(38 - y) + 2.5y = 67

57 - 1.5y + 2.5y = 67

- 1.5y + 2.5y = 67 - 57

y = 10

x = 38 - y = 38 - 10

x = 28

Answer: She bought 28 daises and 10 Tulips.

Step-by-step explanation:

Let x represent the number of daises bought.

Let y represent the number of tulips bought.

Your friend want to have 38 of her favorite flowers. This means that

x + y = 38

Her favorite flowers are daisies at 1.50 each and tulips at 2.50 each if the total bill was 67, it means that

1.5x + 2.5y = 67 - - - - - - - - - - - - 1

Substituting x = 38 - y into equation 1, it becomes

1.5(38 - y) + 2.5y = 67

57 - 1.5y + 2.5y = 67

- 1.5y + 2.5y = 67 - 57

y = 10

x = 38 - y = 38 - 10

x = 28

Help would be nice! Question is can you help me?
All you have to do is find the surface area, free brainliest if you get it right simple as that

No links or stuff like that

Otherwise I will eat your family :)

Answers

Answer:

Step-by-step explanation:

you just got to do 12 * 14 , then divide by 2. so the answer is 84

for the entire thing, the area would be 480

84 please don't eat my family

To find the quotient of 726.02 and 1,000, move the decimal point in 762.02___Places to the ____

Choices for blank 1.

A. 2
B. 3
C. 4
D. 5

Choices for blank 2.

A. Left
B. Right
NO LINKS!!

Answers

from blank one five

from blank two is right

Isabel's team played 8 games of basketball. During those 8 games her team's score was: 59, 65, 61, 64, 68, 57, 49 and 57. What is the median(middle)?

Answers

Answer:

60 :)

Step-by-step explanation:

The middle two numbers are 59 and 61 so you add them together and divide by 2.

PLSS HELP MATH I NEED NOW I WILL GIVE BRAINLIEST TO RIGHT ANSWER

Answers

Answer:

Step-by-step explanation:

If you solve y = -x - 2 you can plot (-4,2)

Hey can someone help me ? I’ll give brainliest !!

Answers

7 bc I’m so smart thank you ciaoooooo

the answer is $23.84. 16 x 1.49 = 23.84

When y=8, the value of y2−4 is

Answers

12

so when y and a number are next to each other it means multiply them.

so 2•8=16

then subtract the 4

16-4

=12

hope this helps

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