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Solve the system of equations
Answer
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$2 x + 5 y = 5$
$- 3 x + 7 y = 36$
$x$Intercept
$\left ( \dfrac { 5 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
$x$Intercept
$\left ( - 12 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 36 } { 7 } \right )$
$\begin{cases} 2x+5y = 5 \\-3x+7y = 36 \end{cases}$
$x = - 5 , y = 3$
Solve quadratic equations using the square root
$\begin{cases} 2 x + 5 y = 5 \\ - 3 x + 7 y = 36 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \\ - 3 x + 7 y = 36 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ y } = \color{#FF6800}{ 36 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - 3 x + 7 y = 36$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ y } = \color{#FF6800}{ 36 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ y } = \color{#FF6800}{ 36 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ Substitute the given $ y $ value into the equation $ x = - \dfrac { 5 } { 2 } y + \dfrac { 5 } { 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + \dfrac { 5 } { 2 }$
$ $ Calculate the product of rational numbers $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 15 } { 2 } } + \dfrac { 5 } { 2 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 15 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } }$
$ $ Find the sum or difference of the fractions $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 36 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 36 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 36 } = \color{#FF6800}{ 36 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 36 } = \color{#FF6800}{ 36 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 3 }$
$ $ 그래프 보기 $ $
Graph
Solution search results
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$ \begin{cases} 2x+y=10 \\ 5x-y=18 \end{cases} $ 
$ \begin{cases} 2x+5y=31 \\ 6x-2y=-26 \end{cases} $
7th-9th grade
Algebra
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