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Solve the system of equations
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Graph
$0.2 x - 0.5 y = - 0.5$
$0.7 x - y = 0.5$
$x$Intercept
$\left ( - \dfrac { 5 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
$x$Intercept
$\left ( \dfrac { 5 } { 7 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 2 } \right )$
$x = 5 , y = 3$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - 0.5 y = - 0.5 \\ 0.7 x - y = 0.5 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } - 0.5 y = - 0.5 \\ 0.7 x - y = 0.5 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \color{#FF6800}{ y } = - 0.5 \\ 0.7 x - y = 0.5 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 2 } } } = - 0.5 \\ 0.7 x - y = 0.5 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \\ 0.7 x - y = 0.5 \end{cases}$
$ $ Convert decimals to fractions $ $
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \\ 0.7 x - y = 0.5 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = - \dfrac { 1 } { 2 } \\ \color{#FF6800}{ 0.7 } \color{#FF6800}{ x } - y = 0.5 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = - \dfrac { 1 } { 2 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } - y = 0.5 \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = - \dfrac { 1 } { 2 } \\ \dfrac { 7 x } { 10 } - y = \color{#FF6800}{ 0.5 } \end{cases}$
$ $ Convert decimals to fractions $ $
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = - \dfrac { 1 } { 2 } \\ \dfrac { 7 x } { 10 } - y = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{cases}$
$\begin{cases} \dfrac { x } { 5 } - \dfrac { y } { 2 } = - \dfrac { 1 } { 2 } \\ \dfrac { 7 x } { 10 } - y = \dfrac { 1 } { 2 } \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \\ \dfrac { 7 x } { 10 } - y = \dfrac { 1 } { 2 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ \dfrac { 7 x } { 10 } - y = \dfrac { 1 } { 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \right ) } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \right ) } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ Substitute the given $ y $ value into the equation $ x = \dfrac { 5 } { 2 } y - \dfrac { 5 } { 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } }$
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } - \dfrac { 5 } { 2 }$
$ $ Calculate the product of rational numbers $ $
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 15 } } { \color{#FF6800}{ 2 } } } - \dfrac { 5 } { 2 }$
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 15 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } }$
$ $ Find the difference between the two fractions $ \dfrac { 15 } { 2 } $ and $ - \dfrac { 5 } { 2 }$
$x = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \\ \color{#FF6800}{ 0.7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0.5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \\ \color{#FF6800}{ 0.7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0.5 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
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