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$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$

$ $ Substitute the given $ y $ value into the equation $ x + 2 y = 8$

$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 8 }$

$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 8 }$

$ $ Solve a solution to $ x$

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 }$

$ $ Substitute the given $ x $ value into the equation $ y = 2 x - 1$

$\color{#FF6800}{ y } = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$

$y = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } - 1$

$ $ Multiply $ 2 $ and $ 2$

$y = \color{#FF6800}{ 4 } - 1$

$y = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$

$ $ Subtract $ 1 $ from $ 4$

$y = \color{#FF6800}{ 3 }$

$\color{#FF6800}{ y } = \color{#FF6800}{ 3 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$

$ $ Check if it is the solution to the system of equations $ $

$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 8 } \end{cases}$

$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 8 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$

$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$

$ $ Since it is true in both equations, it is the solution of the system of equations $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$