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Formula
Solve the system of equations
Graph
$0.2 x - 0.3 y = - 1$
$0.4 x - 5 y = 6.8$
$x$-intercept
$\left ( - 5 , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 10 } { 3 } \right )$
$x$-intercept
$\left ( 17 , 0 \right )$
$y$-intercept
$\left ( 0 , - \dfrac { 34 } { 25 } \right )$
$\begin{cases} 0.2x-0.3y = -1 \\0.4x-5y = 6.8 \end{cases}$
$x = - 8 , y = - 2$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - 0.3 y = - 1 \\ 0.4 x - 5 y = 6.8 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} \color{#FF6800}{ \dfrac { x } { 5 } } - 0.3 y = - 1 \\ 0.4 x - 5 y = 6.8 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ y } = - 1 \\ 0.4 x - 5 y = 6.8 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 y } { 10 } } = - 1 \\ 0.4 x - 5 y = 6.8 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { 3 y } { 10 } = - 1 \\ \color{#FF6800}{ 0.4 } \color{#FF6800}{ x } - 5 y = 6.8 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} \dfrac { x } { 5 } - \dfrac { 3 y } { 10 } = - 1 \\ \color{#FF6800}{ \dfrac { 2 x } { 5 } } - 5 y = 6.8 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { 3 y } { 10 } = - 1 \\ \dfrac { 2 x } { 5 } - 5 y = \color{#FF6800}{ 6.8 } \end{cases}$
 Convert decimals to fractions 
$\begin{cases} \dfrac { x } { 5 } - \dfrac { 3 y } { 10 } = - 1 \\ \dfrac { 2 x } { 5 } - 5 y = \color{#FF6800}{ \dfrac { 34 } { 5 } } \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { 3 y } { 10 } = - 1 \\ \dfrac { 2 x } { 5 } - 5 y = \dfrac { 34 } { 5 } \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \dfrac { 2 x } { 5 } - 5 y = \dfrac { 34 } { 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ \dfrac { 2 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 34 } { 5 } } \end{cases}$
 Substitute the given $x$ value into the equation $\dfrac { 2 x } { 5 } - 5 y = \dfrac { 34 } { 5 }$
$\color{#FF6800}{ \dfrac { 2 \left ( \dfrac { 3 } { 2 } y - 5 \right ) } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 34 } { 5 } }$
$\color{#FF6800}{ \dfrac { 2 \left ( \dfrac { 3 } { 2 } y - 5 \right ) } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 34 } { 5 } }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
 Substitute the given $y$ value into the equation $x = \dfrac { 3 } { 2 } y - 5$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$x = \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - 5$
 Calculate the product of rational numbers 
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } - 5$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Find the sum of the negative numbers 
$x = \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 0.4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = \color{#FF6800}{ 6.8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 0.4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = \color{#FF6800}{ 6.8 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ \dfrac { 34 } { 5 } } = \color{#FF6800}{ \dfrac { 34 } { 5 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ \dfrac { 34 } { 5 } } = \color{#FF6800}{ \dfrac { 34 } { 5 } } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\begin{cases} x = - 8 \\ y = - 2 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 0.4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 6.8 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 44 } { 25 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 44 } { 25 } } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 125 } } \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 176 } { 125 } } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 44 } { 25 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 125 } } \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 176 } { 125 } } \\ - \dfrac { 22 } { 25 } y = \dfrac { 44 } { 25 } \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ - \dfrac { 22 } { 25 } y = \dfrac { 44 } { 25 } \end{cases}$
$\begin{cases} x = - 8 \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 22 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 44 } { 25 } } \end{cases}$
 Solve a solution to $y$
$\begin{cases} x = - 8 \\ \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \end{cases}$
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