Question

Pessoal como faz para obter o ponto de intersecção entre as retas: r:x+2y-3=0 e s: 2x+3y-5=0, a resposta tem que dar P(1,1)

Answer 1

Temos que montar um sistema e resolver:

$\left\{\begin{matrix} x+2y-3=0 & \\ 2x+3y-5=0 & \end{matrix}\right. \\\\ \left\{\begin{matrix} x+2y=3 & \\ 2x+3y=5 & \end{matrix}\right.$

Agora resolvemos:

$\left\{\begin{matrix} x+2y=3 & \Rightarrow x = 3-2y \\ 2x+3y=5 & \end{matrix}\right. \\\\ 2x+3y=5 \\\\ 2(3-2y)+3y = 5 \\\\ 6-4y+3y = 5 \\\\ -y = 5-6 \\\\ -y = -1 \ \ \times -1 \\\\ \boxed{y = 1} \\\\\ \Rightarrow x = 3-2y \\\\ x = 3-2 \cdot (1) \\\\ x = 3-2 \\\\ \boxed{x = 1} \\\\\\ \therefore \boxed{\boxed{P(1,1)}}$