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Formula
Solve the system of equations
Answer
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Graph
$x - 5 y = 8$
$- 7 x + 8 y = 25$
$x$-intercept
$\left ( 8 , 0 \right )$
$y$-intercept
$\left ( 0 , - \dfrac { 8 } { 5 } \right )$
$x$-intercept
$\left ( - \dfrac { 25 } { 7 } , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 25 } { 8 } \right )$
$\begin{cases} x-5y = 8 \\-7x+8y = 25 \end{cases}$
$x = - 7 , y = - 3$
Solve quadratic equations using the square root
$\begin{cases} x - 5 y = 8 \\ - 7 x + 8 y = 25 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ - 7 x + 8 y = 25 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - 7 x + 8 y = 25$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Substitute the given $ y $ value into the equation $ x = 5 y + 8$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 25 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 25 } = \color{#FF6800}{ 25 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\begin{cases} x = - 7 \\ y = - 3 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 25 } \end{cases}$
$ $ Solve the system of linear equations for $ x , y $
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$ $ Solve the system of linear equations for $ x , y $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } = \color{#FF6800}{ 189 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } = \color{#FF6800}{ 189 } \\ - 27 y = 81 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } \\ - 27 y = 81 \end{cases}$
$\begin{cases} x = - 7 \\ \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 81 } \end{cases}$
$ $ Solve a solution to $ y$
$\begin{cases} x = - 7 \\ \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ 그래프 보기 $ $
Graph
Solution search results
search-thumbnail-Equations 
$1 \begin{cases} x+2y=5 \\ 3x+y=5 \end{cases} $ 
$2. \begin{cases} y=x+2 \\ 2x-3y=-7 \end{cases} $ 
$ \begin{cases} 3x-2y=8 \\ x+y=6 \end{cases} $ 
$4$ $ \begin{cases} 2x-3y=-7 \\ 2x-3y=8 \end{cases} $ 
$5$ $ \begin{cases} x-y=-5 \\ x+y=1 \end{cases} $
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