Question

Consideram sistemul
x+ay=1+a
2x+y=3 unde a apartine lui R\ {1/2}.
Demonstrati ca sistemul admite o solutie formata din doua numere egale, oricare ar fi a apartine lui R\{1/2}

Answer 1

x+ay=1+a
2x+y=3

y=3-2x
x+3a-2ax=1+a
x-2ax=1+a-3a
x(1-2a)=1-2a
x=1
y=3-2*1=1