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Solve the system of equations
Answer
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Graph
$x + 6 y = 27$
$7 x - 3 y = 9$
$x$Intercept
$\left ( 27 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 9 } { 2 } \right )$
$x$Intercept
$\left ( \dfrac { 9 } { 7 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 3 \right )$
$\begin{cases} x+6y = 27 \\7x-3y = 9 \end{cases}$
$x = 3 , y = 4$
Solve the system of equations
$\begin{cases} x + 6 y = 27 \\ 7 x - 3 y = 9 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \\ 7 x - 3 y = 9 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \\ \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 9 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 7 x - 3 y = 9$
$\color{#FF6800}{ 7 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 9 }$
$\color{#FF6800}{ 7 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 9 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$ $ Substitute the given $ y $ value into the equation $ x = - 6 y + 27$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 27 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 27 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 3 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 27 } \\ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 9 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 27 } \\ \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 9 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 27 } = \color{#FF6800}{ 27 } \\ \color{#FF6800}{ 9 } = \color{#FF6800}{ 9 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 27 } = \color{#FF6800}{ 27 } \\ \color{#FF6800}{ 9 } = \color{#FF6800}{ 9 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
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