Solving System of Linear Diophantine Equations in three variables

Solving System of Linear Diophantine Equations in three variables by elimination of one variable. Finding general solution of such a system

[@edayahzaid]

thank you so much for your detailed explanations

[@drpriti30]

Thank you for your comment

[@PMAAAbbasMohamed]

Thank you mam

[@drpriti30]

Thank you for watching

[@oskar1818]

Can you explain the part where you introduce t, and how you go from 6(450) = 450-6t

[@drpriti30]

Please check my video on solving diophantine euations in 2 variables. There I have explained how general solution is written in terms of a parameter t. Diophantine equations if solvable have infinite solutions and the different values of t give the infinite solutions

[@akshitkumar3879]

Mam I have a problem that
Prove that x^2 +y^2=z^2
With y even are x=r^2-s^2 , y=2rs , z=r^2+s^2 where r and see are arbitrary integers of opposite parity
Can you prove it

[@drpriti30]

Is this the way
x^2 +y^2 = (r^2-s^2)^2 + (2rs)^2 = r^4 +s^4 -2r^2s^2 + 4r^2s^2
=r^4 +s^4 + 2r^2s^2 = (r^2+s^2)^2 =z^2