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Solve the system of equations
Answer
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$5 x + 7 y = - 1$
$- 3 x + 4 y = - 24$
$x$Intercept
$\left ( - \dfrac { 1 } { 5 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 7 } \right )$
$x$Intercept
$\left ( 8 , 0 \right )$
$y$Intercept
$\left ( 0 , - 6 \right )$
$\begin{cases} 5x+7y = -1 \\-3x+4y = -24 \end{cases}$
$x = 4 , y = - 3$
Solve the system of equations
$\begin{cases} 5 x + 7 y = - 1 \\ - 3 x + 4 y = - 24 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \\ - 3 x + 4 y = - 24 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 24 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ - 3 x + 4 y = - 24$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 24 }$
$ $ 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 = - \dfrac { 7 } { 5 } y - \dfrac { 1 } { 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) - \dfrac { 1 } { 5 }$
$ $ Calculate the product of rational numbers $ $
$x = \color{#FF6800}{ \dfrac { 21 } { 5 } } - \dfrac { 1 } { 5 }$
$x = \color{#FF6800}{ \dfrac { 21 } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } }$
$ $ Find the difference between the two fractions $ \dfrac { 21 } { 5 } $ and $ - \dfrac { 1 } { 5 }$
$x = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 24 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 24 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 24 } = \color{#FF6800}{ - } \color{#FF6800}{ 24 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 24 } = \color{#FF6800}{ - } \color{#FF6800}{ 24 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
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