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Solve the system of equations
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$15 \left ( x + y \right ) = 1$
$9 x + 27 y = 1$
$x$Intercept
$\left ( \dfrac { 1 } { 15 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 15 } \right )$
$x$Intercept
$\left ( \dfrac { 1 } { 9 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 27 } \right )$
$\begin{cases} 15 \left( x+y \right) = 1 \\9x+27y = 1 \end{cases}$
$x = \dfrac { 2 } { 45 } , y = \dfrac { 1 } { 45 }$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ 15 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) = 1 \\ 9 x + 27 y = 1 \end{cases}$
 Multiply each term in parentheses by $15$
$\begin{cases} \color{#FF6800}{ 15 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \color{#FF6800}{ y } = 1 \\ 9 x + 27 y = 1 \end{cases}$
$\begin{cases} 15 x + 15 y = 1 \\ 9 x + 27 y = 1 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } } \\ 9 x + 27 y = 1 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } } \\ \color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 1 } \end{cases}$
 Substitute the given $x$ value into the equation $9 x + 27 y = 1$
$\color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 27 } \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 1 } { 45 } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 1 } { 45 } }$
 Substitute the given $y$ value into the equation $x = - y + \dfrac { 1 } { 15 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 15 } }$
 Find the sum or difference of the fractions 
$x = \color{#FF6800}{ \dfrac { 2 } { 45 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 45 } }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 45 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 1 } { 45 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 45 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 1 } { 45 } }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 15 } \left ( \color{#FF6800}{ \dfrac { 2 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 45 } } \right ) = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 45 } } = \color{#FF6800}{ 1 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 15 } \left ( \color{#FF6800}{ \dfrac { 2 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 45 } } \right ) = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 } { 45 } } \color{#FF6800}{ + } \color{#FF6800}{ 27 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 45 } } = \color{#FF6800}{ 1 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 45 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 1 } { 45 } }$
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