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
0+50x1-60-60x0+10<br> What's the answer
NISA [10]
Following PEDMAS it'd be
=0
0+(50x1)-60-(60x0)+10
0+50-60-0+10
50-60+10
-10+10=0
Hope this helps. :)

4 0
3 years ago
Read 2 more answers
Glen hiked 14 miles in 4 hours. What was his average rate of speed?
Daniel [21]
3.5 miles per hour :) hopefully this helps!
8 0
3 years ago
How long does it take to double a $1,000 investment that pays 6.5% annual interest, compounded monthly?
ahrayia [7]
2p=p(1+0.065/12)^12t
2=(1+0.065/12)^12t
Solve for t
T= [log(2)/ log(1+0.065/12)] /12
T= 10.7 years or if you want to round it would be 11

Answer: 10.7 years or 11 years

Answer: You can use the compound interest formula: A=P(1+interest)^n

A=the new capital
P=the capital invested
n= the #of monthly


Hope this helps (:
3 0
2 years ago
Read 2 more answers
A company's stock price flucated over a period of four days. The table shows the change in stock price per day. The net change i
DiKsa [7]

Answer:

The net change is -.30

Step-by-step explanation:

increase means add

decrease means subtract

+3.50

-3.70

+3.30

-3.40

-------------

-.30

The net change is -.30

7 0
2 years ago
This is what I need help with
siniylev [52]
The answer is 4

3 times 4 equals 12

A way to get the answer is by dividing 12 by 3 and you get 4 as well
4 0
3 years ago
Other questions:
  • Are x^2 and x like terms?
    8·2 answers
  • Sara sells beaded necklaces she makes a profit of 4 dollars pn every neclace she sells which table represents the profit sara ma
    14·1 answer
  • What is .40 = .25 X​
    5·1 answer
  • a wedding reception was being held at Stefanina's restaurant can you please show how you have the answer
    7·2 answers
  • (07.06) Which of the following graphs shows all the possible values for a number that is less than 7? Number line with closed ci
    15·2 answers
  • Evaluate P(4,4) <br> Please help me with this asap. It is timed
    11·1 answer
  • My photo is 8". If I want to reduce it by 12% five times. What is the size of my photo?
    5·1 answer
  • Hello Brainly User please help me I will mark brainliest. Its really east math please help me
    9·1 answer
  • .................................................................................................
    8·1 answer
  • Performing a Rotation in the Coordinate Plane
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!