Verified answer

Resposta:

[tex]x=\dfrac{2}{7}~~~~e~~~~ y=\dfrac{2}{7}[/tex]

Explicação passo a passo:

[tex]\large\displaystyle\begin{cases}\dfrac{x-y}{5}=\dfrac{x-y}{2}~~~~\to I\\ \\ 2x=2-5y~~~~\to II\end[/tex]

Preparando  a 1º

[tex]5(x-y)=2(x-y)\\ \\ 5x-5y=2x-2y\\ \\ 5x-2x-5y+2y=0\\ \\\boxed{ 3x-3y=0~~~I}[/tex]

isolando x na 2º

[tex]2x=2-5y\\ \\\boxed{ x=\dfrac{2-5y}{2}}[/tex]

Substituir x na 1º

[tex]3x-3y=0\\ \\ 3.(\dfrac{2-5y}{2})-3y=0\\ \\\\ \dfrac{6-15y}{2}-3y=0\\ \\ \\ 6-15y-3y=0\\ \\ -21y=-6\\ \\ y=\dfrac{-21}{-6}\\ \\ \\\boxed{ y=\dfrac{2}{7}}[/tex]

Substituir y em:

[tex]3x-3y=0\\ \\ 3x-3.(\dfrac{2}{7})=0\\ \\ \\ 3x-\dfrac{6}{7}=0\\ \\ 21x-6=0\\ \\ 21x=6\\ \\ x=\dfrac{6}{21}\\ \\ \\\boxed{ x=\dfrac{2}{7}}[/tex]