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Solve the system of equations
Answer
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Graph
$7 \left ( 4 + x \right ) = 2 \left ( y - 3 \right )$
$4 \left ( - x - y \right ) = 7 - y$
$x$Intercept
$\left ( - \dfrac { 34 } { 7 } , 0 \right )$
$y$Intercept
$\left ( 0 , 17 \right )$
$x$Intercept
$\left ( - \dfrac { 7 } { 4 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 7 } { 3 } \right )$
$\begin{cases} 7 \left( 4+x \right) = 2 \left( y-3 \right) \\4 \left( -x-y \right) = 7-y \end{cases}$
$x = - 4 , y = 3$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \\ \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ y } \end{cases}$
$ $ Organize the expression $ $
$\begin{cases} \color{#FF6800}{ 28 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ y } \end{cases}$
$\begin{cases} 28 + 7 x = 2 y - 6 \\ - 4 x - 4 y = 7 - y \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } } \\ - 4 x - 4 y = 7 - y \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } } \\ \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ y } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - 4 x - 4 y = 7 - y$
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ y }$
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ y }$
$ $ 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 { 2 } { 7 } y - \dfrac { 34 } { 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } }$
$x = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } - \dfrac { 34 } { 7 }$
$ $ Calculate the product of rational numbers $ $
$x = \color{#FF6800}{ \dfrac { 6 } { 7 } } - \dfrac { 34 } { 7 }$
$x = \color{#FF6800}{ \dfrac { 6 } { 7 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 7 } }$
$ $ Find the difference between the two fractions $ \dfrac { 6 } { 7 } $ and $ - \dfrac { 34 } { 7 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \\ \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \\ \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 0 } = \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 4 } = \color{#FF6800}{ 4 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 0 } = \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 4 } = \color{#FF6800}{ 4 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
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