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
Solve by graphing:<br> x^2-6x+9=0
irinina [24]
Hello :
the solution :x²-6x+9=0 is the x- intresept and graph of f(x) =x²-6x+9
the solution is :  x=3

6 0
2 years ago
Which word sentence represents the equation?
Pavlova-9 [17]
<span>Hello :)

6(x+3)=(x+3)+(x+3)+(x+3)+(x+3)+(x+3)+(x+3)
Six times some number plus 3 is 42.</span>
8 0
3 years ago
Read 2 more answers
Flying against the wind, an airplane travels 3760 kilometers in 4 hours. Flying with the wind, the same plane travels 4320 kilom
Gemiola [76]

Answer:

1 hour each 30 minutes so the answer is 30 minutes

5 0
2 years ago
In the following figure lines j and k are parallel and are cut by transversal t<br><br> Thanks
Sedbober [7]

angle 1 and angle 7 are alternate exterior angles.

angle 1 and angle 5 are corresponding angles.

angle 3 and angle 8 are same side interior angles.

angle 2 and angle 8 are alternate interior angles.

4 0
3 years ago
Please thank you so much yall
Leto [7]
19. There are 24 hours in a day and Maria travelled for 15 days so multiply the two:
24*15=360

So Maria travelled for 360 hours.


22a. False; 2,000 lbs = 1 Ton
22c. True; 48 oz = 3 lbs
4 0
3 years ago
Read 2 more answers
Other questions:
  • the coordinates of the vertices of triangle ABC are a (-2,2), b (5,-3), c (-4,-1). Identify the perimeter of triangle ABC.
    8·1 answer
  • which function results after applying the sequence of transformations to f(x)=x^5 reflect over the y axis ; shift 1 unit left ;
    12·2 answers
  • Let f(x) =x^2+10x+29<br><br><br> What is the minimum value of the function?<br><br><br> ____
    12·1 answer
  • Can someone explain to me how to solve this ​
    11·1 answer
  • One fifth of a number is subtracted from four fifth of the same number. If the result is 9, what is the number. ​
    6·1 answer
  • A pet store sold 74 puppies in a week if each puppy is $ 65 how much money would they have made
    12·2 answers
  • Help please will give brainiest
    13·1 answer
  • Find m∠1 - Its Geometry
    11·1 answer
  • Geometry - Similar
    10·1 answer
  • If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogra
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!