Question

sa se rezolve sistemul

1999x+2000y=1999
2000x+1999y=2000

Answer 1

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Answer 2

2 000 x + 1 999 y = 2 000

1 999 x + 2 000 y = 1 999

_____________________ → scad relatiile si le adun

( 2 000 x - 1 999 x ) + ( 1 999 y - 2 000 y ) = 2 000 - 1 999

( 2 000 x + 1 999 x ) + ( 1 999 y + 2 000 y ) = 2 000 + 1 999

3 999 x + 3 999 y = 3 999 l : 3 999

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{x - y = 1 ⇒ x = y + 1

{x + y = 1

________

( y + 1 ) + y = 1

2 y = 1 - 1

y = 0

x = 0 + 1

x = 1

Solutii: x = 1 si y = 0

Verific: 1 999 × 1 + 2 000 × 0 = 1 999