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Solve the system of equations
Answer
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$x + y = 800$
$\dfrac { 9 } { 100 } x + \dfrac { 13 } { 100 } y = 80$
$x$Intercept
$\left ( 800 , 0 \right )$
$y$Intercept
$\left ( 0 , 800 \right )$
$x$Intercept
$\left ( \dfrac { 8000 } { 9 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 8000 } { 13 } \right )$
$x = 600 , y = 200$
Solve the system of equations
$\begin{cases} x + y = 800 \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ x } + \dfrac { 13 } { 100 } y = 80 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} x + y = 800 \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ x } } { \color{#FF6800}{ 100 } } } + \dfrac { 13 } { 100 } y = 80 \end{cases}$
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ y } = 80 \end{cases}$
$ $ Calculate the multiplication expression $ $
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } \color{#FF6800}{ y } } { \color{#FF6800}{ 100 } } } = 80 \end{cases}$
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \\ \dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ x } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } \color{#FF6800}{ y } } { \color{#FF6800}{ 100 } } } = \color{#FF6800}{ 80 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ \dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \right ) } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } \color{#FF6800}{ y } } { \color{#FF6800}{ 100 } } } = \color{#FF6800}{ 80 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \right ) } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } \color{#FF6800}{ y } } { \color{#FF6800}{ 100 } } } = \color{#FF6800}{ 80 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 800$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ 800 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ 800 }$
$ $ Add $ - 200 $ and $ 800$
$x = \color{#FF6800}{ 600 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ 200 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 80 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ 200 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } } { \color{#FF6800}{ 100 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 80 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 80 } = \color{#FF6800}{ 80 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 80 } = \color{#FF6800}{ 80 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
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