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Solve the system of equations
Graph
$5 x + 2 y = 10$
$2 x + 5 y = 8$
$x$Intercept
$\left ( 2 , 0 \right )$
$y$Intercept
$\left ( 0 , 5 \right )$
$x$Intercept
$\left ( 4 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 8 } { 5 } \right )$
$\begin{cases} 5x+2y = 10 \\2x+5y = 8 \end{cases}$
$x = \dfrac { 34 } { 21 } , y = \dfrac { 20 } { 21 }$
Solve quadratic equations using the square root
$\begin{cases} 5 x + 2 y = 10 \\ 2 x + 5 y = 8 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \\ 2 x + 5 y = 8 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 } \end{cases}$
 Substitute the given $x$ value into the equation $2 x + 5 y = 8$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ y } = \color{#FF6800}{ 8 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 20 } { 21 } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 20 } { 21 } }$
 Substitute the given $y$ value into the equation $x = - \dfrac { 2 } { 5 } y + 2$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } + 2$
 Calculate the product of rational numbers 
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 8 } { 21 } } + 2$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 8 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Get the subtract 
$x = \color{#FF6800}{ \dfrac { 34 } { 21 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 34 } { 21 } }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 34 } { 21 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 20 } { 21 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 34 } { 21 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 20 } { 21 } }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 34 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 34 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 34 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 34 } { 21 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 21 } } = \color{#FF6800}{ 8 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 8 } = \color{#FF6800}{ 8 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 34 } { 21 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 20 } { 21 } }$
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