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Solve the system of equations
Answer
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Graph
$x = y + 15$
$60 x = 90 y$
$x$Intercept
$\left ( 15 , 0 \right )$
$y$Intercept
$\left ( 0 , - 15 \right )$
$x$Intercept
$\left ( 0 , 0 \right )$
$y$Intercept
$\left ( 0 , 0 \right )$
$\begin{cases} x = y+15 \\60x = 90y \end{cases}$
$x = 45 , y = 30$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \\ \color{#FF6800}{ 60 } \color{#FF6800}{ x } = \color{#FF6800}{ 90 } \color{#FF6800}{ y } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 60 x = 90 y$
$\color{#FF6800}{ 60 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \right ) = \color{#FF6800}{ 90 } \color{#FF6800}{ y }$
$\color{#FF6800}{ 60 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \right ) = \color{#FF6800}{ 90 } \color{#FF6800}{ y }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 30 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 30 }$
$ $ Substitute the given $ y $ value into the equation $ x = y + 15$
$\color{#FF6800}{ x } = \color{#FF6800}{ 30 } \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
$x = \color{#FF6800}{ 30 } \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
$ $ Add $ 30 $ and $ 15$
$x = \color{#FF6800}{ 45 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 45 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 45 } , \color{#FF6800}{ y } = \color{#FF6800}{ 30 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 45 } , \color{#FF6800}{ y } = \color{#FF6800}{ 30 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 45 } = \color{#FF6800}{ 30 } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \\ \color{#FF6800}{ 60 } \color{#FF6800}{ \times } \color{#FF6800}{ 45 } = \color{#FF6800}{ 90 } \color{#FF6800}{ \times } \color{#FF6800}{ 30 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 45 } = \color{#FF6800}{ 30 } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \\ \color{#FF6800}{ 60 } \color{#FF6800}{ \times } \color{#FF6800}{ 45 } = \color{#FF6800}{ 90 } \color{#FF6800}{ \times } \color{#FF6800}{ 30 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 45 } = \color{#FF6800}{ 45 } \\ \color{#FF6800}{ 2700 } = \color{#FF6800}{ 2700 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 45 } = \color{#FF6800}{ 45 } \\ \color{#FF6800}{ 2700 } = \color{#FF6800}{ 2700 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 45 } , \color{#FF6800}{ y } = \color{#FF6800}{ 30 }$
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