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Solve the system of equations

Answer

Graph

$0.3 x + 0.4 y = 1.7$

$\dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3$

$x$Intercept

$\left ( \dfrac { 17 } { 3 } , 0 \right )$

$y$Intercept

$\left ( 0 , \dfrac { 17 } { 4 } \right )$

$x$Intercept

$\left ( \dfrac { 9 } { 2 } , 0 \right )$

$y$Intercept

$\left ( 0 , 6 \right )$

$x = 3 , y = 2$

Solve the system of equations

$\begin{cases} \color{#FF6800}{ 0.3 } \color{#FF6800}{ x } + 0.4 y = 1.7 \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$ $ Calculate the multiplication expression $ $

$\begin{cases} \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } + 0.4 y = 1.7 \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$\begin{cases} \dfrac { 3 x } { 10 } + \color{#FF6800}{ 0.4 } \color{#FF6800}{ y } = 1.7 \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$ $ Calculate the multiplication expression $ $

$\begin{cases} \dfrac { 3 x } { 10 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ y } } { \color{#FF6800}{ 5 } } } = 1.7 \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \color{#FF6800}{ 1.7 } \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$ $ Convert decimals to fractions $ $

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 10 } } } \\ \dfrac { 2 } { 3 } x + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \dfrac { 17 } { 10 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ x } + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$ $ Calculate the multiplication expression $ $

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \dfrac { 17 } { 10 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } { \color{#FF6800}{ 3 } } } + \dfrac { 1 } { 2 } y = 3 \end{cases}$

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \dfrac { 17 } { 10 } \\ \dfrac { 2 x } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ y } = 3 \end{cases}$

$ $ Calculate the multiplication expression $ $

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \dfrac { 17 } { 10 } \\ \dfrac { 2 x } { 3 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 2 } } } = 3 \end{cases}$

$\begin{cases} \dfrac { 3 x } { 10 } + \dfrac { 2 y } { 5 } = \dfrac { 17 } { 10 } \\ \dfrac { 2 x } { 3 } + \dfrac { y } { 2 } = 3 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 3 } } } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ 3 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ \dfrac { 2 x } { 3 } + \dfrac { y } { 2 } = 3$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 3 } } } \right ) } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ y } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ 3 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

$ $ Substitute the given $ y $ value into the equation $ x = - \dfrac { 4 } { 3 } y + \dfrac { 17 } { 3 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 3 } } }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } + \dfrac { 17 } { 3 }$

$ $ Calculate the product of rational numbers $ $

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 3 } } } + \dfrac { 17 } { 3 }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 3 } } }$

$ $ Find the sum or difference of the fractions $ $

$x = \color{#FF6800}{ 3 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 3 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

$ $ Check if it is the solution to the system of equations $ $

$\begin{cases} \color{#FF6800}{ 0.3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 0.4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 1.7 } \\ \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 3 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 10 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 17 } } { \color{#FF6800}{ 10 } } } \\ \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \end{cases}$

$ $ Since it is true in both equations, it is the solution of the system of equations $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

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