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Formula
Solve the system of equations
Graph
$x - 5 y = 8$
$- 7 x + 8 y = 25$
$x$-intercept
$\left ( 8 , 0 \right )$
$y$-intercept
$\left ( 0 , - \dfrac { 8 } { 5 } \right )$
$x$-intercept
$\left ( - \dfrac { 25 } { 7 } , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 25 } { 8 } \right )$
$\begin{cases} x-5y = 8 \\-7x+8y = 25 \end{cases}$
$x = - 7 , y = - 3$
Solve quadratic equations using the square root
$\begin{cases} x - 5 y = 8 \\ - 7 x + 8 y = 25 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ - 7 x + 8 y = 25 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 } \end{cases}$
 Substitute the given $x$ value into the equation $- 7 x + 8 y = 25$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
 Substitute the given $y$ value into the equation $x = 5 y + 8$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\begin{cases} x = - 7 \\ y = - 3 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } = \color{#FF6800}{ 189 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } = \color{#FF6800}{ 189 } \\ - 27 y = 81 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } \\ - 27 y = 81 \end{cases}$
$\begin{cases} x = - 7 \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
 Solve a solution to $y$
$\begin{cases} x = - 7 \\ \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
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