Plot 87x-64y=3 on the Cartesian Graph:
Slope intercept form:
Slope intercept form: y = mx + b
y = 1.359375x - 0.046875
Solve the following over the integers
87x - 64y = 3
Use Euclids Algorithm in Rewritten Form:
Calculate the GCF of (87,-64)
Diophantine Table:
| # | Quotient1 | Quotient2 | Remainder1 | Remainder2 | Remainder | Final | Rewritten |
|---|---|---|---|---|---|---|---|
| 1 | 87/-64 | -2 | 87 - (-64 x -2) | 87 - 128 | -41 | 87 = -2 x -64 + -41 | -41 = 87 - -2 x -64 |
| 2 | -64/-41 | 1 | -64 - (-41 x 1) | -64 - -41 | -23 | -64 = 1 x -41 + -23 | -23 = -64 - 1 x -41 |
| 3 | -41/-23 | 1 | -41 - (-23 x 1) | -41 - -23 | -18 | -41 = 1 x -23 + -18 | -18 = -41 - 1 x -23 |
| 4 | -23/-18 | 1 | -23 - (-18 x 1) | -23 - -18 | -5 | -23 = 1 x -18 + -5 | -5 = -23 - 1 x -18 |
| 5 | -18/-5 | 3 | -18 - (-5 x 3) | -18 - -15 | -3 | -18 = 3 x -5 + -3 | -3 = -18 - 3 x -5 |
| 6 | -5/-3 | 1 | -5 - (-3 x 1) | -5 - -3 | -2 | -5 = 1 x -3 + -2 | -2 = -5 - 1 x -3 |
| 7 | -3/-2 | 1 | -3 - (-2 x 1) | -3 - -2 | -1 | -3 = 1 x -2 + -1 | -1 = -3 - 1 x -2 |
| 8 | -2/-1 | 2 | -2 - (-1 x 2) | -2 - -2 | 0 | -2 = 2 x -1 + 0 | 0 = -2 - 2 x -1 |
GCF (87, -64) = -1
Rearrange to solve in terms of GCF = -1
-1 = -3 - 1 x -2
Substitute our rewrite value for -2
-3 - 1(-5 - 1 x -3)
Multiply the items inside our parentheses by 1
-2 = -5 - 1 x -3
Substitute our rewrite value for -3
-5 - 1(-18 - 3 x -5)
Multiply the items inside our parentheses by 1
-3 = -18 - 3 x -5
Substitute our rewrite value for -5
-18 - 3(-23 - 1 x -18)
Multiply the items inside our parentheses by 3
-5 = -23 - 1 x -18
Substitute our rewrite value for -18
-23 - 1(-41 - 1 x -23)
Multiply the items inside our parentheses by 1
-18 = -41 - 1 x -23
Substitute our rewrite value for -23
-41 - 1(-64 - 1 x -41)
Multiply the items inside our parentheses by 1
-23 = -64 - 1 x -41
Substitute our rewrite value for -41
-64 - 1(87 - -2 x -64)
Multiply the items inside our parentheses by 1
-41 = 87 - -2 x -64
Substitute our rewrite value for
87 - -2()
Multiply the items inside our parentheses by -2
Final Answers
How does the Diophantine Equations Calculator work?
This calculator has 1 input.
What 1 formula is used for the Diophantine Equations Calculator?
What 4 concepts are covered in the Diophantine Equations Calculator?
- diophantine equations
- equation
- a statement declaring two mathematical expressions are equal
- multiply
- to add equal groups
* - substitution
- a simple way to solve linear equations algebraically and find the solutions of the variables.
