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Solve the system of equations
Answer
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$8 x - y = 49$
$3 x + 2 y = - 3$
$x$Intercept
$\left ( \dfrac { 49 } { 8 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 49 \right )$
$x$Intercept
$\left ( - 1 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 3 } { 2 } \right )$
$\begin{cases} 8x-y = 49 \\3x+2y = -3 \end{cases}$
$x = 5 , y = - 9$
Solve quadratic equations using the square root
$\begin{cases} 8 x - y = 49 \\ 3 x + 2 y = - 3 \end{cases}$
$ $ Solve a solution to $ y$
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 49 } \\ 3 x + 2 y = - 3 \end{cases}$
$\begin{cases} \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 49 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Substitute the given $ y $ value into the equation $ 3 x + 2 y = - 3$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 49 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 49 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$ $ Substitute the given $ x $ value into the equation $ y = 8 x - 49$
$\color{#FF6800}{ y } = \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 49 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 49 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right ) = \color{#FF6800}{ 49 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right ) = \color{#FF6800}{ 49 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 49 } = \color{#FF6800}{ 49 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 49 } = \color{#FF6800}{ 49 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ 그래프 보기 $ $
Graph
Solution search results
search-thumbnail-Solve the following systems by elimination. 
$1$ $ \begin{cases} x+3y=-1 \\ 3x+9y=-3 \end{cases} $ 
$2$ $ \begin{cases} x+4y+8=0 \\ 3x-2y-4=0 \end{cases} $ 
$3$ $ \begin{cases} 3x-y=4 \\ 5x+2y=-1 \end{cases} $
7th-9th grade
Algebra
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