# Calculator search results

Formula
Solve the system of equations
Graph
$x + y = 800$
$\dfrac { 9 } { 100 } x + \dfrac { 13 } { 100 } y = 80$
$x$-intercept
$\left ( 800 , 0 \right )$
$y$-intercept
$\left ( 0 , 800 \right )$
$x$-intercept
$\left ( \dfrac { 8000 } { 9 } , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 8000 } { 13 } \right )$
$\begin{cases} x+y = 800 \\ \dfrac{ 9 }{ 100 } x+ \dfrac{ 13 }{ 100 } y = 80 \end{cases}$
$x = 600 , y = 200$
Solve quadratic equations using the square root
$\begin{cases} x + y = 800 \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ x } + \dfrac { 13 } { 100 } y = 80 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} x + y = 800 \\ \color{#FF6800}{ \dfrac { 9 x } { 100 } } + \dfrac { 13 } { 100 } y = 80 \end{cases}$
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \color{#FF6800}{ \dfrac { 13 } { 100 } } \color{#FF6800}{ y } = 80 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \color{#FF6800}{ \dfrac { 13 y } { 100 } } = 80 \end{cases}$
$\begin{cases} x + y = 800 \\ \dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \\ \dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 9 x } { 100 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 y } { 100 } } = \color{#FF6800}{ 80 } \end{cases}$
 Substitute the given $x$ value into the equation $\dfrac { 9 x } { 100 } + \dfrac { 13 y } { 100 } = 80$
$\color{#FF6800}{ \dfrac { 9 \left ( - y + 800 \right ) } { 100 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 y } { 100 } } = \color{#FF6800}{ 80 }$
$\color{#FF6800}{ \dfrac { 9 \left ( - y + 800 \right ) } { 100 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 y } { 100 } } = \color{#FF6800}{ 80 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
 Substitute the given $y$ value into the equation $x = - y + 800$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ 800 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ 800 }$
 Add $- 200$ and $800$
$x = \color{#FF6800}{ 600 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ 200 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 80 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ 200 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 600 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 80 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 80 } = \color{#FF6800}{ 80 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 80 } = \color{#FF6800}{ 80 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ 600 } , \color{#FF6800}{ y } = \color{#FF6800}{ 200 }$
$\begin{cases} x = 600 \\ y = 200 \end{cases}$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 } { 100 } } \color{#FF6800}{ y } = \color{#FF6800}{ 80 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
 Solve the system of linear equations for $x , y$
$\begin{cases} \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ x } = \color{#FF6800}{ 24 } \\ \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ x } = \color{#FF6800}{ 24 } \\ \dfrac { 1 } { 25 } y = 8 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 600 } \\ \dfrac { 1 } { 25 } y = 8 \end{cases}$
$\begin{cases} x = 600 \\ \color{#FF6800}{ \dfrac { 1 } { 25 } } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
 Solve a solution to $y$
$\begin{cases} x = 600 \\ \color{#FF6800}{ y } = \color{#FF6800}{ 200 } \end{cases}$
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