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Solve the system of equations
Answer
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Graph
$x + y = 150$
$1000 x + 500 y = 117500$
$x$Intercept
$\left ( 150 , 0 \right )$
$y$Intercept
$\left ( 0 , 150 \right )$
$x$Intercept
$\left ( \dfrac { 235 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , 235 \right )$
$\begin{cases} x+y = 150 \\1000x+500y = 117500 \end{cases}$
$x = 85 , y = 65$
Solve the system of equations
$\begin{cases} x + y = 150 \\ 1000 x + 500 y = 117500 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 150 } \\ 1000 x + 500 y = 117500 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 150 } \\ \color{#FF6800}{ 1000 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 500 } \color{#FF6800}{ y } = \color{#FF6800}{ 117500 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 1000 x + 500 y = 117500$
$\color{#FF6800}{ 1000 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 150 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 500 } \color{#FF6800}{ y } = \color{#FF6800}{ 117500 }$
$\color{#FF6800}{ 1000 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 150 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 500 } \color{#FF6800}{ y } = \color{#FF6800}{ 117500 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 65 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 65 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 150$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 65 } \color{#FF6800}{ + } \color{#FF6800}{ 150 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 65 } \color{#FF6800}{ + } \color{#FF6800}{ 150 }$
$ $ Add $ - 65 $ and $ 150$
$x = \color{#FF6800}{ 85 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 85 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 85 } , \color{#FF6800}{ y } = \color{#FF6800}{ 65 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 85 } , \color{#FF6800}{ y } = \color{#FF6800}{ 65 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 85 } \color{#FF6800}{ + } \color{#FF6800}{ 65 } = \color{#FF6800}{ 150 } \\ \color{#FF6800}{ 1000 } \color{#FF6800}{ \times } \color{#FF6800}{ 85 } \color{#FF6800}{ + } \color{#FF6800}{ 500 } \color{#FF6800}{ \times } \color{#FF6800}{ 65 } = \color{#FF6800}{ 117500 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 85 } \color{#FF6800}{ + } \color{#FF6800}{ 65 } = \color{#FF6800}{ 150 } \\ \color{#FF6800}{ 1000 } \color{#FF6800}{ \times } \color{#FF6800}{ 85 } \color{#FF6800}{ + } \color{#FF6800}{ 500 } \color{#FF6800}{ \times } \color{#FF6800}{ 65 } = \color{#FF6800}{ 117500 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 150 } = \color{#FF6800}{ 150 } \\ \color{#FF6800}{ 117500 } = \color{#FF6800}{ 117500 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 150 } = \color{#FF6800}{ 150 } \\ \color{#FF6800}{ 117500 } = \color{#FF6800}{ 117500 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 85 } , \color{#FF6800}{ y } = \color{#FF6800}{ 65 }$
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