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Solve the system of equations
Answer
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$x - 5 y = 8$
$- 7 x + 8 y = 25$
$x$Intercept
$\left ( 8 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 8 } { 5 } \right )$
$x$Intercept
$\left ( - \dfrac { 25 } { 7 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 25 } { 8 } \right )$
$\begin{cases} x-5y = 8 \\-7x+8y = 25 \end{cases}$
$x = - 7 , y = - 3$
Solve the system of equations
$\begin{cases} x - 5 y = 8 \\ - 7 x + 8 y = 25 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ - 7 x + 8 y = 25 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - 7 x + 8 y = 25$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Substitute the given $ y $ value into the equation $ x = 5 y + 8$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
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