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Formula
Solve the system of equations
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$\dfrac { x } { 100 } \times 100 + \dfrac { y } { 100 } \times 200 = 21$
$\dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24$
$x$Intercept
$\left ( 21 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 21 } { 2 } \right )$
$x$Intercept
$\left ( 12 , 0 \right )$
$y$Intercept
$\left ( 0 , 24 \right )$
$\begin{cases} \dfrac{ x }{ 100 } \times 100+ \dfrac{ y }{ 100 } \times 200 = 21 \\ \dfrac{ x }{ 100 } \times 200+ \dfrac{ y }{ 100 } \times 100 = 24 \end{cases}$
$x = 9 , y = 6$
Solve quadratic equations using the square root
$\begin{cases} \color{#FF6800}{ \dfrac { x } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } + \dfrac { y } { 100 } \times 200 = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { x } { 100 } } + \dfrac { y } { 100 } \times 200 = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} \color{#FF6800}{ 100 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { x } { 100 } } + \dfrac { y } { 100 } \times 200 = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} \color{#FF6800}{ x } + \dfrac { y } { 100 } \times 200 = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} x + \color{#FF6800}{ \dfrac { y } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Simplify the expression 
$\begin{cases} x + \color{#FF6800}{ 200 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { y } { 100 } } = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} x + \color{#FF6800}{ 200 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { y } { 100 } } = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} x + \color{#FF6800}{ 2 } \color{#FF6800}{ y } = 21 \\ \dfrac { x } { 100 } \times 200 + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} x + 2 y = 21 \\ \color{#FF6800}{ \dfrac { x } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Simplify the expression 
$\begin{cases} x + 2 y = 21 \\ \color{#FF6800}{ 200 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { x } { 100 } } + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} x + 2 y = 21 \\ \color{#FF6800}{ 200 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { x } { 100 } } + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} x + 2 y = 21 \\ \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \dfrac { y } { 100 } \times 100 = 24 \end{cases}$
$\begin{cases} x + 2 y = 21 \\ 2 x + \color{#FF6800}{ \dfrac { y } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } = 24 \end{cases}$
 Simplify the expression 
$\begin{cases} x + 2 y = 21 \\ 2 x + \color{#FF6800}{ 100 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { y } { 100 } } = 24 \end{cases}$
$\begin{cases} x + 2 y = 21 \\ 2 x + \color{#FF6800}{ 100 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { y } { 100 } } = 24 \end{cases}$
 Calculate the multiplication expression 
$\begin{cases} x + 2 y = 21 \\ 2 x + \color{#FF6800}{ y } = 24 \end{cases}$
$\begin{cases} x + 2 y = 21 \\ 2 x + y = 24 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 21 } \\ 2 x + y = 24 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 21 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 24 } \end{cases}$
 Substitute the given $x$ value into the equation $2 x + y = 24$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 21 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 24 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 21 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } = \color{#FF6800}{ 24 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
 Substitute the given $y$ value into the equation $x = - 2 y + 21$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 21 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 21 }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ 9 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 9 }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ 9 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 9 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 21 } \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } = \color{#FF6800}{ 24 } \end{cases}$
$\begin{cases} \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } = \color{#FF6800}{ 21 } \\ \color{#FF6800}{ \dfrac { 9 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 200 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 6 } { 100 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } = \color{#FF6800}{ 24 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 21 } = \color{#FF6800}{ 21 } \\ \color{#FF6800}{ 24 } = \color{#FF6800}{ 24 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 21 } = \color{#FF6800}{ 21 } \\ \color{#FF6800}{ 24 } = \color{#FF6800}{ 24 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ 9 } , \color{#FF6800}{ y } = \color{#FF6800}{ 6 }$
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