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Formula
Solve the system of equations
Graph
$10 x + 18 y = - 11$
$16 x - 9 y = - 5$
$x$Intercept
$\left ( - \dfrac { 11 } { 10 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 11 } { 18 } \right )$
$x$Intercept
$\left ( - \dfrac { 5 } { 16 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 5 } { 9 } \right )$
$\begin{cases} 10x+18y = -11 \\16x-9y = -5 \end{cases}$
$x = - \dfrac { 1 } { 2 } , y = - \dfrac { 1 } { 3 }$
Solve the system of equations
$\begin{cases} 10 x + 18 y = - 11 \\ 16 x - 9 y = - 5 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } } \\ 16 x - 9 y = - 5 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } } \\ \color{#FF6800}{ 16 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \end{cases}$
 Substitute the given $x$ value into the equation $16 x - 9 y = - 5$
$\color{#FF6800}{ 16 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 16 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
 Substitute the given $y$ value into the equation $x = - \dfrac { 9 } { 5 } y - \dfrac { 11 } { 10 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 5 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) - \dfrac { 11 } { 10 }$
 Calculate the product of rational numbers 
$x = \color{#FF6800}{ \dfrac { 3 } { 5 } } - \dfrac { 11 } { 10 }$
$x = \color{#FF6800}{ \dfrac { 3 } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 } { 10 } }$
 Find the difference between the two fractions $\dfrac { 3 } { 5 }$ and $- \dfrac { 11 } { 10 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 18 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \\ \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 18 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \\ \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 11 } = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 5 } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 11 } = \color{#FF6800}{ - } \color{#FF6800}{ 11 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 5 } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
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