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Formula
Solve the system of equations
Answer
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Graph
$x - y = 3$
$x + y = 5$
$x$-intercept
$\left ( 3 , 0 \right )$
$y$-intercept
$\left ( 0 , - 3 \right )$
$x$-intercept
$\left ( 5 , 0 \right )$
$y$-intercept
$\left ( 0 , 5 \right )$
$\begin{cases} x-y = 3 \\x+y = 5 \end{cases}$
$x = 4 , y = 1$
Solve quadratic equations using the square root
$\begin{cases} x - y = 3 \\ x + y = 5 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \\ x + y = 5 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \\ \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ x + y = 5$
$\left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$\left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 5 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$ $ Substitute the given $ y $ value into the equation $ x = y + 3$
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$x = \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ 1 $ and $ 3$
$x = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 1 }$
$\begin{cases} x = 4 \\ y = 1 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 5 } \end{cases}$
$ $ Solve the system of linear equations for $ x , y $
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ 2 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } = \color{#FF6800}{ 3 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ 2 } \end{cases}$
$ $ Solve the system of linear equations for $ x , y $
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ 8 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ 2 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ 8 } \\ 2 y = 2 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ 2 y = 2 \end{cases}$
$\begin{cases} x = 4 \\ \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ 2 } \end{cases}$
$ $ Solve a solution to $ y$
$\begin{cases} x = 4 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 1 } \end{cases}$
$ $ 그래프 보기 $ $
Graph
Solution search results
search-thumbnail-$1$ $ \begin{cases} x-y=3 \\ x-y=5 \end{cases} $ 
YA 

$4$ 
$3$ 
$2$ 

$4$ $-3$ $-2$ $.1$ 
$-4$ $2$ $3$ $5$ $2$ 
$-2$ 
$-3$ 
$4$ 
$5$
7th-9th grade
Other
search-thumbnail-Equations 
$1 \begin{cases} x+2y=5 \\ 3x+y=5 \end{cases} $ 
$2. \begin{cases} y=x+2 \\ 2x-3y=-7 \end{cases} $ 
$ \begin{cases} 3x-2y=8 \\ x+y=6 \end{cases} $ 
$4$ $ \begin{cases} 2x-3y=-7 \\ 2x-3y=8 \end{cases} $ 
$5$ $ \begin{cases} x-y=-5 \\ x+y=1 \end{cases} $
7th-9th grade
Other
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