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Formula
Solve the system of equations
Graph
$5 x + 3 y = 17$
$x = y - 3$
$x$-intercept
$\left ( \dfrac { 17 } { 5 } , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 17 } { 3 } \right )$
$x$-intercept
$\left ( - 3 , 0 \right )$
$y$-intercept
$\left ( 0 , 3 \right )$
$\begin{cases} 5x+3y = 17 \\x = y-3 \end{cases}$
$x = 1 , y = 4$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
 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 
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$\begin{cases} x = 1 \\ y = 4 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} 5 x + 3 y = 17 \\ \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
 Do transposition 
$\begin{cases} 5 x + 3 y = 17 \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 40 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 40 } \\ - 8 y = - 32 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 1 } \\ - 8 y = - 32 \end{cases}$
$\begin{cases} x = 1 \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$
 Solve a solution to $y$
$\begin{cases} x = 1 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 4 } \end{cases}$
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