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Solve the system of equations
Answer
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Graph
$x + y = 730$
$- \dfrac { 5 } { 100 } x + \dfrac { 6 } { 100 } y = 2$
$x$Intercept
$\left ( 730 , 0 \right )$
$y$Intercept
$\left ( 0 , 730 \right )$
$x$Intercept
$\left ( - 40 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 100 } { 3 } \right )$
$\begin{cases} x+y = 730 \\- \dfrac{ 5 }{ 100 } x+ \dfrac{ 6 }{ 100 } y = 2 \end{cases}$
$x = 380 , y = 350$
Solve the system of equations
$\begin{cases} x + y = 730 \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 100 } } \color{#FF6800}{ x } + \dfrac { 6 } { 100 } y = 2 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} x + y = 730 \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 20 } } + \dfrac { 6 } { 100 } y = 2 \end{cases}$
$\begin{cases} x + y = 730 \\ - \dfrac { x } { 20 } + \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ y } = 2 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} x + y = 730 \\ - \dfrac { x } { 20 } + \color{#FF6800}{ \dfrac { 3 y } { 50 } } = 2 \end{cases}$
$\begin{cases} x + y = 730 \\ - \dfrac { x } { 20 } + \dfrac { 3 y } { 50 } = 2 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 730 } \\ - \dfrac { x } { 20 } + \dfrac { 3 y } { 50 } = 2 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 730 } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 20 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 y } { 50 } } = \color{#FF6800}{ 2 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - \dfrac { x } { 20 } + \dfrac { 3 y } { 50 } = 2$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { - y + 730 } { 20 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 y } { 50 } } = \color{#FF6800}{ 2 }$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { - y + 730 } { 20 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 y } { 50 } } = \color{#FF6800}{ 2 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 350 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 350 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 730$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 350 } \color{#FF6800}{ + } \color{#FF6800}{ 730 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 350 } \color{#FF6800}{ + } \color{#FF6800}{ 730 }$
$ $ Add $ - 350 $ and $ 730$
$x = \color{#FF6800}{ 380 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 380 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 380 } , \color{#FF6800}{ y } = \color{#FF6800}{ 350 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 380 } , \color{#FF6800}{ y } = \color{#FF6800}{ 350 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 380 } \color{#FF6800}{ + } \color{#FF6800}{ 350 } = \color{#FF6800}{ 730 } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 380 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 350 } = \color{#FF6800}{ 2 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 380 } \color{#FF6800}{ + } \color{#FF6800}{ 350 } = \color{#FF6800}{ 730 } \\ \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 380 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 350 } = \color{#FF6800}{ 2 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 730 } = \color{#FF6800}{ 730 } \\ \color{#FF6800}{ 2 } = \color{#FF6800}{ 2 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 730 } = \color{#FF6800}{ 730 } \\ \color{#FF6800}{ 2 } = \color{#FF6800}{ 2 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 380 } , \color{#FF6800}{ y } = \color{#FF6800}{ 350 }$
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