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Solve the system of equations
Answer
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$7 x - 2 y = - 4$
$5 x - 4 y = 10$
$x$Intercept
$\left ( - \dfrac { 4 } { 7 } , 0 \right )$
$y$Intercept
$\left ( 0 , 2 \right )$
$x$Intercept
$\left ( 2 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 5 } { 2 } \right )$
$\begin{cases} 7x-2y = -4 \\5x-4y = 10 \end{cases}$
$x = - 2 , y = - 5$
Solve quadratic equations using the square root
$\begin{cases} 7 x - 2 y = - 4 \\ 5 x - 4 y = 10 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } } \\ 5 x - 4 y = 10 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } } \\ \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 10 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 5 x - 4 y = 10$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 10 }$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 10 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ Substitute the given $ y $ value into the equation $ x = \dfrac { 2 } { 7 } y - \dfrac { 4 } { 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } }$
$x = \color{#FF6800}{ \dfrac { 2 } { 7 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) - \dfrac { 4 } { 7 }$
$ $ Calculate the product of rational numbers $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 10 } { 7 } } - \dfrac { 4 } { 7 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 10 } { 7 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 7 } }$
$ $ Find the sum or difference of the fractions $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) = \color{#FF6800}{ 10 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) = \color{#FF6800}{ 10 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 4 } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 4 } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ 그래프 보기 $ $
Graph
Solution search results
search-thumbnail-
$ \begin{cases} 2x+y=10 \\ 5x-y=18 \end{cases} $ 
$ \begin{cases} 2x+5y=31 \\ 6x-2y=-26 \end{cases} $
7th-9th grade
Algebra
search-thumbnail-$\left(1\right)$ $ \begin{cases} x+2y=7 \\ 3x-2y=13 \end{cases} $ 
$\left(3\right)$ $ \begin{cases} 3x+2y=-9 \\ 2x-4y=10 \end{cases} $
10th-13th grade
Other
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