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Solve the system of equations
Answer
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$x - \dfrac { y - 5 } { 2 } = 8$
$\dfrac { 5 } { 6 } x - \dfrac { y } { 4 } = \dfrac { 19 } { 4 }$
$x$Intercept
$\left ( \dfrac { 11 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 11 \right )$
$x$Intercept
$\left ( \dfrac { 57 } { 10 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 19 \right )$
$x = 6 , y = 1$
Solve the system of equations
$\begin{cases} x - \dfrac { y - 5 } { 2 } = 8 \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ x } - \dfrac { y } { 4 } = \dfrac { 19 } { 4 } \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} x - \dfrac { y - 5 } { 2 } = 8 \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } } { \color{#FF6800}{ 6 } } } - \dfrac { y } { 4 } = \dfrac { 19 } { 4 } \end{cases}$
$\begin{cases} x - \dfrac { y - 5 } { 2 } = 8 \\ \dfrac { 5 x } { 6 } - \dfrac { y } { 4 } = \dfrac { 19 } { 4 } \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } } \\ \dfrac { 5 x } { 6 } - \dfrac { y } { 4 } = \dfrac { 19 } { 4 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ \dfrac { 5 x } { 6 } - \dfrac { y } { 4 } = \dfrac { 19 } { 4 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } } \right ) } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } } \right ) } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$ $ Substitute the given $ y $ value into the equation $ x = \dfrac { 1 } { 2 } y + \dfrac { 11 } { 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } } { \color{#FF6800}{ 2 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 19 } } { \color{#FF6800}{ 4 } } } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
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