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Solve the system of equations
Answer
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Graph
$x + y = 10$
$10 x + 8 y = 88$
$x$Intercept
$\left ( 10 , 0 \right )$
$y$Intercept
$\left ( 0 , 10 \right )$
$x$Intercept
$\left ( \dfrac { 44 } { 5 } , 0 \right )$
$y$Intercept
$\left ( 0 , 11 \right )$
$x = 4 , y = 6$
Solve the system of equations
$\begin{cases} x + y = 10 \\ 10 x + 8 y = 88 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ 10 x + 8 y = 88 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 10 x + 8 y = 88$
$\color{#FF6800}{ 10 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 }$
$\color{#FF6800}{ 10 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 10$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$ $ Add $ - 6 $ and $ 10$
$x = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } = \color{#FF6800}{ 88 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } = \color{#FF6800}{ 88 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 88 } = \color{#FF6800}{ 88 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 88 } = \color{#FF6800}{ 88 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
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