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Formula
Solve the system of equations
$\begin{cases} w-2z = 10 \\2w+3z = -8 \end{cases}$
$w = 2 , z = - 4$
Solve quadratic equations using the square root
$\begin{cases} w - 2 z = 10 \\ 2 w + 3 z = - 8 \end{cases}$
 Solve a solution to $w$
$\begin{cases} \color{#FF6800}{ w } = \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ 2 w + 3 z = - 8 \end{cases}$
$\begin{cases} \color{#FF6800}{ w } = \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ w } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \end{cases}$
 Substitute the given $w$ value into the equation $2 w + 3 z = - 8$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ z } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
 Solve a solution to $z$
$\color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
 Substitute the given $z$ value into the equation $w = 2 z + 10$
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
 Organize the expression 
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 }$
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 }$
 The possible solutions are as follows 
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 } , \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 } , \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ w } = \color{#FF6800}{ 2 } , \color{#FF6800}{ z } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
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