Question

me ajudem? por favor

Answer 1

$\left \{ {\big{\cfrac{5x-2}{2}+\cfrac{y-3}{5}=2x\ \ \ (1)} \atop \big{\cfrac{7(y-1)}{2}+\cfrac{x-5}{3}=2y\ \ \ (2)}} \right.$

De (1) temos:

$\cfrac{5x-2}{2}+\cfrac{y-3}{5}=2x \Rightarrow \cfrac{5(5x-2)+2(y-3)}{10} = 2x \\ \\ 5(5x-2)+2(y-3) = 20x \\ 25x -10 +2y-6 = 20x \\ 5x +2y-16 = 0\\ 2y = 16 -5x \\ y = \cfrac{16 -5x}{2}\ \ \ (3)$

De (2) temos:

$\cfrac{7(y-1)}{2}+\cfrac{x-5}{3}=2y \Rightarrow \cfrac{3\cdot 7(y-1) + 2(x-5)}{6} = 2y \\ \cfrac{21y -21+2x-10}{6} = 2y$

Substituindo y de (3) vem:

$\cfrac{21\bigg(\cfrac{16 -5x}{2}\bigg) -21+2x-10}{6} = 16 - 5x \\ \\ 21\bigg(8-\cfrac{5x}{2}\bigg)+2x-31= 96-30x \\ 168 - \cfrac{105x}{2}+32x=127 \\ - \cfrac{105x}{2}+32x = -41 \\ -105x+64x=-82 \\ -41x = -82 \Longrightarrow \boxed{x = 2}$

Substituindo x em (3) temos:

$y = \cfrac{16 -5x}{2} = \cfrac{16 -5(2)}{2} = \cfrac{6}{2} \Longrightarrow \boxed{y = 3}$