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