Question

Qual é o ponto de encontro entre duas retas concorrentes cujas equações são:
y= 2x+1 e y= 2-3x?

Answer 1

No ponto de encontro, a coordenada "y" (e a coordenada "x") das duas retas será igual, logo:

$y_{reta_1}~=~y_{reta_2}\\\\\\2x+1~=~2-3x\\\\\\2x+3x~=~2-1\\\\\\5x~=~1\\\\\\\boxed{x~=~\frac{1}{5}}\\\\\\\\Substituindo~"x"~em~uma~das~equacoes~(qualquer~uma~das~duas):\\\\\\y~=~2x+1\\\\\\y~=~2\,.\,\frac{1}{5}~+~1\\\\\\y~=~\frac{2}{5}~+~1\\\\\\\boxed{y~=~\frac{7}{5}}$

Resposta: O ponto de encontro será (x,y) = (1/5 , 7/5)