Question

resolva os sistemas.​

Answer 1

Resposta:

a)

$x + y = 6 \\ \frac{x}{2} + \frac{y}{3} = \frac{8}{3} \\ \\ x = 6 - y \\ \\ \frac{6 - y}{2} + \frac{y}{3} = \frac{8}{3} \\ \frac{18 - 3y + 2y}{6} = \frac{8}{3} \\ \frac{18 - y}{6} = \frac{8}{3} \\ (18 - y) \times 3 = 8 \times 6 \\ 54 - 3y = 48 \\ 54 - 48 = 3y \\ 6 = 3y \\ y = \frac{6}{3} \\ y = 2 \\ \\ x = 6 - y \\ x = 6 - 2 \\ x = 4$

b)

$x = 4 + y \\ \frac{x}{2} + \frac{y}{5} = 2 \\ \\ \frac{4 + y}{2} + \frac{y}{5} = 2 \\ \frac{20 + 5y + 2y}{10} = 2 \\ \frac{20 + 7y}{10} = 2 \\ 10 \times 2 = 20 + 7y \\ 20 = 20 + 7y \\ 0 = 7y \\ y = 0 \\ \\ x = 4 + y \\ x = 4$

c)

$y = x - 2 \\ \frac{x}{5} + y = \frac{8}{5} \\ \\ \frac{x}{5} + x - 2 = \frac{8}{5} \\ \frac{x + 5x - 10x}{5} = \frac{8}{5} \\ \frac{x - 5x}{5} = \frac{8}{5} \\ x - 5x = 8 \\ - 4x = 8 \\ x = - 2 \\ \\ y = x - 2 \\ y = - 2 - 2 \\ y = - 4$