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$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ 5 x + 3 y = 17$

$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 }$

$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 }$

$ $ Solve a solution to $ y$

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

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

$ $ Substitute the given $ y $ value into the equation $ x = y - 3$

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$

$x = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$

$ $ Subtract $ 3 $ from $ 4$

$x = \color{#FF6800}{ 1 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$

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

$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$

$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 17 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$

$\begin{cases} \color{#FF6800}{ 17 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$

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

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$