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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 the system of equations

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

$ $ 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 $ $

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

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