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Formula
Solve the system of equations
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$95 x + 20 y = 800$
$20 x - 4 y = - 100$
$x$Intercept
$\left ( \dfrac { 160 } { 19 } , 0 \right )$
$y$Intercept
$\left ( 0 , 40 \right )$
$x$Intercept
$\left ( - 5 , 0 \right )$
$y$Intercept
$\left ( 0 , 25 \right )$
$\begin{cases} 95x+20y = 800 \\20x-4y = -100 \end{cases}$
$x = \dfrac { 20 } { 13 } , y = \dfrac { 425 } { 13 }$
Solve quadratic equations using the square root
$\begin{cases} 95 x + 20 y = 800 \\ 20 x - 4 y = - 100 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } } \\ 20 x - 4 y = - 100 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } } \\ \color{#FF6800}{ 20 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 100 } \end{cases}$
 Substitute the given $x$ value into the equation $20 x - 4 y = - 100$
$\color{#FF6800}{ 20 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 100 }$
$\color{#FF6800}{ 20 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 100 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 425 } { 13 } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 425 } { 13 } }$
 Substitute the given $y$ value into the equation $x = - \dfrac { 4 } { 19 } y + \dfrac { 160 } { 19 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 4 } { 19 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } + \dfrac { 160 } { 19 }$
 Calculate the product of rational numbers 
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1700 } { 247 } } + \dfrac { 160 } { 19 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1700 } { 247 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 160 } { 19 } }$
 Find the sum or difference of the fractions 
$x = \color{#FF6800}{ \dfrac { 20 } { 13 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 20 } { 13 } }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 20 } { 13 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 425 } { 13 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 20 } { 13 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 425 } { 13 } }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 95 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 13 } } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 20 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 13 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } = \color{#FF6800}{ - } \color{#FF6800}{ 100 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 95 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 13 } } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ 20 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 20 } { 13 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 425 } { 13 } } = \color{#FF6800}{ - } \color{#FF6800}{ 100 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 100 } = \color{#FF6800}{ - } \color{#FF6800}{ 100 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 800 } = \color{#FF6800}{ 800 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 100 } = \color{#FF6800}{ - } \color{#FF6800}{ 100 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 20 } { 13 } } , \color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 425 } { 13 } }$
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