1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivenika [448]
3 years ago
9

Using the Extended Euclidean Algorithm, find integers x and y such that 26x + 9y = 1.

Mathematics
1 answer:
Xelga [282]3 years ago
8 0

Answer:

The solution is: x=-1 and y=3.

Step-by-step explanation:

Let's find the solution, but first let's remember the following:

A / B = C + R where:

A=dividend, B=divisor, C=quotient, and R=remainder. This can be express as follows:

A = (C * B) + R, which is the structure we are going to use next.

Using the Euclidian Algorithm we need to find the highst common factor (HCF) between the coefficients from your equation, this means:

The original equation: 26x+9y=1 is in the form Ax+By=C, so A=26, B=9 and C=1.

We need to find the HCF of 'A' and 'B'. Using the Euclidan Algorithm (EA), so we have:

A = (C * B) + R, using our values:

26 = (2 * 9) + 8, look that the divisor (B) is 9 and the remainder (R) is 8.

Now using the (EA) we divide the divisor (B=9) by the obtained remainder (R=8). And we do the same for each obtained result until the las remainder (R) is equal to 0, like this:

A = (C * B) + R

9 = (8 * 1) + 1

using the divisor (B=8) and the remainder (R=1) we obtain:

A = (C * B) + R

8 = (1 * 8) + 0, look that the remainder is now 0, so in summary we can use the method as follows:

26 = (2 * 9) + 8

9 = (8 * 1) + 1

8 = (1 * 8) + 0; and this equations are the ones we are going to use in order to find a solution.

Next step is to use the equation before R=0, so:

9 = (8 * 1) + 1, which is:

9 - (8 * 1) = 1; but if you consider the first obtained equation: 26 = (2 * 9) + 8, we can write:

26 - (2 * 9) = 8, and we can use this expression in the previous one, so:

9 - (8 * 1) = 1, is:

9 - ((26 - (2 * 9)) * 1) = 1, simplifying:

9 - 26 + (2*9) = 1

9 - 26 + (9 + 9) = 1

-26 + (9 + 9 + 9) = 1

-26 + (3 * 9) = 1

26*(-1) + 9*(3) = 1; if you compare the last expression with the original equation, which is: 26x+9y=1, you can see the similarity, where x=-1 and y=3.

So, the solution is: x=-1 and y=3.

You might be interested in
Isla flipped a coin 30 times. The coin landed heads up 9 times and tails up 21 times.
DedPeter [7]

A.) Either way the probability would be 1/2 because there are only 2 sides of a coin so fate decides on which side it will land on.


B.)Same as A

8 0
3 years ago
If C{1,2} and D={4,5,6}, find C×D by tabulation method. i need for exam​
Katarina [22]

Answer:

Step-by-step explanation:

C * D = {(x,y): x is an element of C and y is an element of D.}

C * D = { (1,4), (1,5), (1,6), (2,4), (2,5), (2,6) }

4 0
2 years ago
Solve: 5(2+2x)-3x>17
Vikentia [17]

Answer:

10+10x-3x>17

10+7x>17

7x>17-10

7x>7

x>1

Hope it helps:-)

3 0
3 years ago
PLZ SOLVE ASAP Solve for f. -11f=7(1-2f)+5
viktelen [127]

Answer:

f = 4

Step-by-step explanation:

Step 1: Distribute

-11f = 7 - 14f + 5

Step 2: Combine like terms

-11f = 12 - 14f

Step 3: Add 14f to both sides

3f = 12

Step 4: Divide both sides by 3

f = 4

4 0
3 years ago
Read 2 more answers
In an aquarium,2/5 of fish are surgeon. Of these ,3/4 are yellow tangs.what fraction of all fish in the aquarium are yellow tang
hoa [83]
8 are surgeon, 15 are yellow tangs
8 0
3 years ago
Other questions:
  • 5ry - c = q<br> solve for r
    11·1 answer
  • A school is organizing a cookout where
    7·1 answer
  • Which statements about this prism partially packed with unit cubes are true? Check all that apply.
    9·2 answers
  • If you need 20 feet of tile and each tile measures a half a foot how many tiles do you need to get?
    10·2 answers
  • A goat is placed in a circular pen with a radius of 15 feet. The formula for the area of a circle is A=πr2, where r is the radiu
    9·1 answer
  • A double cheeseburger has 540 calories, a milk shake has 490 calories and a serving of fries has 380 calories. If you burn 130 c
    13·1 answer
  • A nest of ants has been growing exponentially in such a way that its population, P, as a function of w weeks is given by P(w)=24
    5·1 answer
  • At a store, a hat has a regular price of x dollars. During a sale, the price of the hat is discounted by 20%.
    7·1 answer
  • R^2-3r-54=0
    7·1 answer
  • An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!