Question

Resolva o sistema de equação abaixo:
{2(x+y)=5(x-y)
{$\frac{x}{2}$-y-2=0

Answer 1

Resposta:

2(x+y)=5(x-y)

2x+2y= 5x-5y

2y+5y=5x-2x

7y= 3x

y=3x/7

substituindo na segunda sentença, temos

$\frac{x}{2} - \frac{3x}{7} - 2 = 0 \\ \frac{7x - 6x}{14} = 2 \\ x = 2 .14 = 28$

$y = \frac{3. 28}{7} = 3.4 = 12$

Answer 2

$\begin{cases}2(x+y)=5(x-y)\\\dfrac{x}{2}-y-2=0\end{cases}$

$\begin{cases}2x+2y=5x-5y\\x-2y-4=0\end{cases}$

$\begin{cases} 5x-2x-5y-2y=0\\x-2y=4\end{cases}$

$\begin{cases}3x-7y=0\\x-2y=4\end{cases}$

$+\underline{\begin{cases}3x-7y=0\\-3x+6y=-12\end{cases}}$

$-y=-12\times(-1)$

$\boxed{\boxed{\mathsf{y=12}}}$

$x-2y=4\\x-2.12=4\\x-24=4\\x=24+4$

$\boxed{\boxed{\mathsf{x=28}}}$

$\boxed{\boxed{\mathsf{s=\{28,12\}}}}$