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Formula
Solve the equation
Graph
$2 x + 3 y = 16$
$x$Intercept
$\left ( 8 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 16 } { 3 } \right )$
$2x+3y = 16$
$x = - \dfrac { 3 } { 2 } y + 8$
 Solve a solution to $x$
$2 x \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = 16$
 Move the rest of the expression except $x$ term to the right side and replace the sign 
$2 x = 16 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right )$
$2 x = \color{#FF6800}{ 16 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ y } \right )$
 Organize the expression 
$2 x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 16 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 16 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 2 }$
$x = \left ( - 3 y + 16 \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 2 }$
 Convert division to multiplication 
$x = \left ( - 3 y + 16 \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$x = \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
 Multiply each term in parentheses by $\dfrac { 1 } { 2 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } + 16 \times \dfrac { 1 } { 2 }$
 Simplify the expression 
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ y } + 16 \times \dfrac { 1 } { 2 }$
$x = - \dfrac { 3 } { 2 } y + \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
 Calculate the product of rational numbers 
$x = - \dfrac { 3 } { 2 } y + \color{#FF6800}{ 8 }$
$y = - \dfrac { 2 } { 3 } x + \dfrac { 16 } { 3 }$
 Solve a solution to $y$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } + 3 y = 16$
 Move the rest of the expression except $y$ term to the right side and replace the sign 
$3 y = 16 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right )$
$3 y = \color{#FF6800}{ 16 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right )$
 Organize the expression 
$3 y = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 16 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 16 }$
 Divide both sides by the same number 
$\color{#FF6800}{ y } = \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 3 }$
$y = \left ( - 2 x + 16 \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 3 }$
 Convert division to multiplication 
$y = \left ( - 2 x + 16 \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
$y = \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
 Multiply each term in parentheses by $\dfrac { 1 } { 3 }$
$y = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
$y = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } } + 16 \times \dfrac { 1 } { 3 }$
 Simplify the expression 
$y = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ x } + 16 \times \dfrac { 1 } { 3 }$
$y = - \dfrac { 2 } { 3 } x + \color{#FF6800}{ 16 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } }$
 Calculate the product of rational numbers 
$y = - \dfrac { 2 } { 3 } x + \color{#FF6800}{ \dfrac { 16 } { 3 } }$
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