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Solve the system of equations

Answer

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$x + y = 10$

$10 x + 8 y = 88$

$x$-intercept

$\left ( 10 , 0 \right )$

$y$-intercept

$\left ( 0 , 10 \right )$

$x$-intercept

$\left ( \dfrac { 44 } { 5 } , 0 \right )$

$y$-intercept

$\left ( 0 , 11 \right )$

$\begin{cases} x+y = 10 \\10x+8y = 88 \end{cases}$

$x = 4 , y = 6$

Solve quadratic equations using the square root

$\begin{cases} x + y = 10 \\ 10 x + 8 y = 88 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ 10 x + 8 y = 88 \end{cases}$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ 10 x + 8 y = 88$

$\color{#FF6800}{ 10 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ 6 }$

$ $ Substitute the given $ y $ value into the equation $ x = - y + 10$

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$

$ $ Add $ - 6 $ and $ 10$

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

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

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$

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

$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } = \color{#FF6800}{ 88 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 88 } = \color{#FF6800}{ 88 } \end{cases}$

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

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$

$\begin{cases} x = 4 \\ y = 6 \end{cases}$

Solve quadratic equations using the square root

$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ y } = \color{#FF6800}{ 88 } \end{cases}$

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

$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \end{cases}$

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

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \end{cases}$

$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \\ - 2 y = - 12 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \\ - 2 y = - 12 \end{cases}$

$\begin{cases} x = 4 \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 12 } \end{cases}$

$ $ Solve a solution to $ y$

$\begin{cases} x = 4 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 6 } \end{cases}$

$ $ 그래프 보기 $ $

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