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Solve the system of equations
Answer
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Graph
$x = y - 8$
$x = - 2 y + 7$
$x$Intercept
$\left ( - 8 , 0 \right )$
$y$Intercept
$\left ( 0 , 8 \right )$
$x$Intercept
$\left ( 7 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 7 } { 2 } \right )$
$\begin{cases} x = y-8 \\x = -2y+7 \end{cases}$
$x = - 3 , y = 5$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ x = - 2 y + 7$
$\color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 8 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 8 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 7 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Substitute the given $ y $ value into the equation $ x = y - 8$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$x = \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$ $ Subtract $ 8 $ from $ 5$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
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