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Solve the system of equations

Answer

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$5 x + 3 y = 17$

$x = y - 3$

$x$-intercept

$\left ( \dfrac { 17 } { 5 } , 0 \right )$

$y$-intercept

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

$x$-intercept

$\left ( - 3 , 0 \right )$

$y$-intercept

$\left ( 0 , 3 \right )$

$\begin{cases} 5x+3y = 17 \\x = y-3 \end{cases}$

$x = 1 , y = 4$

Solve quadratic equations using the square root

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

$ $ Substitute the given $ x $ value into the equation $ 5 x + 3 y = 17$

$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ 4 }$

$ $ Substitute the given $ y $ value into the equation $ x = y - 3$

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$

$x = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$

$ $ Subtract $ 3 $ from $ 4$

$x = \color{#FF6800}{ 1 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$

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

$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 17 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$

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

$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$

$\begin{cases} x = 1 \\ y = 4 \end{cases}$

Solve quadratic equations using the square root

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

$ $ Do transposition $ $

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

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

$ $ Solve the system of linear equations for $ x , y $

$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$

$ $ Solve the system of linear equations for $ x , y $

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 40 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 40 } \\ - 8 y = - 32 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 1 } \\ - 8 y = - 32 \end{cases}$

$\begin{cases} x = 1 \\ \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 32 } \end{cases}$

$ $ Solve a solution to $ y$

$\begin{cases} x = 1 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 4 } \end{cases}$

$ $ 그래프 보기 $ $

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