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Answer

↓Steps Explained:↓

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

-2 = -5 - 1 x -3

Multiply the items inside our parentheses by 1

Substitute our rewrite value for -3

-3 = -18 - 3 x -5

Multiply the items inside our parentheses by 1

Substitute our rewrite value for -5

-5 = -23 - 1 x -18

Multiply the items inside our parentheses by 3

Substitute our rewrite value for -18

-18 = -41 - 1 x -23

Multiply the items inside our parentheses by 1

Substitute our rewrite value for -23

-23 = -64 - 1 x -41

Multiply the items inside our parentheses by 1

Substitute our rewrite value for -41

-41 = 87 - -2 x -64

Multiply the items inside our parentheses by 1

Substitute our rewrite value for

87 - -2()

Multiply the items inside our parentheses by -2

Final Answers