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Solve the system of equations
Answer
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Graph
$x + y = 30$
$x - y = 8$
$x$Intercept
$\left ( 30 , 0 \right )$
$y$Intercept
$\left ( 0 , 30 \right )$
$x$Intercept
$\left ( 8 , 0 \right )$
$y$Intercept
$\left ( 0 , - 8 \right )$
$\begin{cases} x+y = 30 \\x-y = 8 \end{cases}$
$x = 19 , y = 11$
Solve quadratic equations using the square root
$\begin{cases} x + y = 30 \\ x - y = 8 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \\ x - y = 8 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ x - y = 8$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 8 }$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 8 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 11 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 11 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 30$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$ $ Add $ - 11 $ and $ 30$
$x = \color{#FF6800}{ 19 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 19 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 19 } , \color{#FF6800}{ y } = \color{#FF6800}{ 11 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 19 } , \color{#FF6800}{ y } = \color{#FF6800}{ 11 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } = \color{#FF6800}{ 30 } \\ \color{#FF6800}{ 19 } \color{#FF6800}{ - } \color{#FF6800}{ 11 } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 11 } = \color{#FF6800}{ 30 } \\ \color{#FF6800}{ 19 } \color{#FF6800}{ - } \color{#FF6800}{ 11 } = \color{#FF6800}{ 8 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 30 } = \color{#FF6800}{ 30 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 30 } = \color{#FF6800}{ 30 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 19 } , \color{#FF6800}{ y } = \color{#FF6800}{ 11 }$
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