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Formula

Solve the system of equations

Answer

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$4 y + 3 x = 8$

$8 x - 9 y = - 77$

$x$-intercept

$\left ( \dfrac { 8 } { 3 } , 0 \right )$

$y$-intercept

$\left ( 0 , 2 \right )$

$x$-intercept

$\left ( - \dfrac { 77 } { 8 } , 0 \right )$

$y$-intercept

$\left ( 0 , \dfrac { 77 } { 9 } \right )$

$\begin{cases} 4y+3x = 8 \\8x-9y = -77 \end{cases}$

$x = - 4 , y = 5$

Solve quadratic equations using the square root

$\begin{cases} 4 y + 3 x = 8 \\ 8 x - 9 y = - 77 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 3 } } \\ 8 x - 9 y = - 77 \end{cases}$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 3 } } \\ \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 77 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ 8 x - 9 y = - 77$

$\color{#FF6800}{ 8 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 3 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 77 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ 5 }$

$ $ Substitute the given $ y $ value into the equation $ x = - \dfrac { 4 } { 3 } y + \dfrac { 8 } { 3 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 3 } }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } + \dfrac { 8 } { 3 }$

$ $ Calculate the product of rational numbers $ $

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 20 } { 3 } } + \dfrac { 8 } { 3 }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 20 } { 3 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 3 } }$

$ $ Find the sum or difference of the fractions $ $

$x = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$

$ $ Check if it is the solution to the system of equations $ $

$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } = \color{#FF6800}{ - } \color{#FF6800}{ 77 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 77 } = \color{#FF6800}{ - } \color{#FF6800}{ 77 } \end{cases}$

$ $ Since it is true in both equations, it is the solution of the system of equations $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$

$\begin{cases} x = - 4 \\ y = 5 \end{cases}$

Solve quadratic equations using the square root

$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 77 } \end{cases}$

$ $ Solve the system of linear equations for $ x , y $

$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 59 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 295 } \end{cases}$

$ $ Solve the system of linear equations for $ x , y $

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 177 } \color{#FF6800}{ x } = \color{#FF6800}{ 708 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 59 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 295 } \end{cases}$

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 177 } \color{#FF6800}{ x } = \color{#FF6800}{ 708 } \\ - 59 y = - 295 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ - 59 y = - 295 \end{cases}$

$\begin{cases} x = - 4 \\ \color{#FF6800}{ - } \color{#FF6800}{ 59 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 295 } \end{cases}$

$ $ Solve a solution to $ y$

$\begin{cases} x = - 4 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 5 } \end{cases}$

$ $ 그래프 보기 $ $

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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} $

7th-9th grade

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