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Solve the system of equations
Answer
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Graph
$x + y = 10$
$3 x + y = 20$
$x$Intercept
$\left ( 10 , 0 \right )$
$y$Intercept
$\left ( 0 , 10 \right )$
$x$Intercept
$\left ( \dfrac { 20 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , 20 \right )$
$\begin{cases} x+y = 10 \\3x+y = 20 \end{cases}$
$x = 5 , y = 5$
Solve the system of equations
$\begin{cases} x + y = 10 \\ 3 x + y = 20 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ 3 x + y = 20 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 20 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 3 x + y = 20$
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 20 }$
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 20 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 10$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$ $ Add $ - 5 $ and $ 10$
$x = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 20 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 20 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 20 } = \color{#FF6800}{ 20 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 20 } = \color{#FF6800}{ 20 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
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