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Solve the system of equations
Answer
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Graph
$x + 2 y = 1$
$x + 4 y = 5$
$x$Intercept
$\left ( 1 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 2 } \right )$
$x$Intercept
$\left ( 5 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 5 } { 4 } \right )$
$x = - 3 , y = 2$
Solve the system of equations
$\begin{cases} x + 2 y = 1 \\ x + 4 y = 5 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \\ x + 4 y = 5 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ x + 4 y = 5$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 2 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 2 }$
$ $ Substitute the given $ y $ value into the equation $ x = - 2 y + 1$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$
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