Can someone solve the equation 619x +401y = 1, where x and y are integers?

Answer 1

Yes. This is a two-step process, and goes like this:

619 = (1)401 + 218
401 = (1)218 + 183
218 = (1)183 + 35
183 = (5)35 + 8
35 = (4)8 + 3
8 = (2)3 + 2
3 = (1)2 + 1

Now, working backwards from the last equation, using substitution, and factoring, you get:

1 = 3 - (1)2
= 3 - (1)[8 - (2)3]
= (3)3 - (1)8
= (3)[35 - (4)8] - (1)8
= (3)35 - (13)8
= (3)35 - (13)[183 - (5)35]
= (68)35 - (13)183
= (68)[218 - (1)183] - (13)183
= (68)218 - (81)183
= (68)218 - (81)[401 - (1)218]
= (149)218 - (81)401
= (149)[619 - (1)401] - (81)401
= (149)619 - (230)401

So, (149)619 - (230)401 = 1, and therefore, x = 149 and y = -230. There may be other solutions to this equation.

Answer 2

Simplifying
619x + 401y = 1

Solving
619x + 401y = 1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-401y' to each side of the equation.
619x + 401y + -401y = 1 + -401y

Combine like terms: 401y + -401y = 0
619x + 0 = 1 + -401y
619x = 1 + -401y

Divide each side by '619'.
x = 0.001615508885 + -0.647819063y

Simplifying
x = 0.001615508885 + -0.647819063y
P.S. These have fractional equivalents as well.

Answer 3

This is a simple equation of a straight line whose normal form is Y=mX + b. Put it in that form by moving the X to the Right hand side by subtracting it from both sides:
401y = -619x + 1

Then divide thru by 401 to get
Y = -619/401 X + 1/401
That is the equation of the straight line. You can now plot it
(or solve it) for any X by substituting in X and calculating Y.

Answer 4

You have two variables x and y and only one equation. So, you can only express x in terms of y.

619x + 410y = 1

x = ( 1 - 410 y ) / 619

Answer 5

There are infinite number of solutions.