Solve the System of Equations 14=3y+x , 20=2y-3x

$14 = 3 y + x$ , $20 = 2 y - 3 x$

Solve for $x$ in $14 = 3 y + x$ .

Rewrite the equation as $3 y + x = 14$ .

$3 y + x = 14$

$20 = 2 y - 3 x$

Subtract $3 y$ from both sides of the equation.

$x = 14 - 3 y$

$20 = 2 y - 3 x$

$x = 14 - 3 y$

$20 = 2 y - 3 x$

Replace all occurrences of $x$ with $14 - 3 y$ in each equation.

Replace all occurrences of $x$ in $20 = 2 y - 3 x$ with $14 - 3 y$ .

$20 = 2 y - 3 (14 - 3 y)$

$x = 14 - 3 y$

Simplify the right side.

Simplify $2 y - 3 (14 - 3 y)$ .

Simplify each term.

Apply the distributive property.

$20 = 2 y - 3 \cdot 14 - 3 (- 3 y)$

$x = 14 - 3 y$

Multiply $- 3$ by $14$ .

$20 = 2 y - 42 - 3 (- 3 y)$

$x = 14 - 3 y$

Multiply $- 3$ by $- 3$ .

$20 = 2 y - 42 + 9 y$

$x = 14 - 3 y$

$20 = 2 y - 42 + 9 y$

$x = 14 - 3 y$

Add $2 y$ and $9 y$ .

$20 = 11 y - 42$

$x = 14 - 3 y$

$20 = 11 y - 42$

$x = 14 - 3 y$

$20 = 11 y - 42$

$x = 14 - 3 y$

$20 = 11 y - 42$

$x = 14 - 3 y$

Solve for $y$ in $20 = 11 y - 42$ .

Rewrite the equation as $11 y - 42 = 20$ .

$11 y - 42 = 20$

$x = 14 - 3 y$

Move all terms not containing $y$ to the right side of the equation.

Add $42$ to both sides of the equation.

$11 y = 20 + 42$

$x = 14 - 3 y$

Add $20$ and $42$ .

$11 y = 62$

$x = 14 - 3 y$

$11 y = 62$

$x = 14 - 3 y$

Divide each term in $11 y = 62$ by $11$ and simplify.

Divide each term in $11 y = 62$ by $11$ .

$\frac{11 y}{11} = \frac{62}{11}$

$x = 14 - 3 y$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{62}{11}$

$x = 14 - 3 y$

Divide $y$ by $1$ .

$y = \frac{62}{11}$

$x = 14 - 3 y$

$y = \frac{62}{11}$

$x = 14 - 3 y$

$y = \frac{62}{11}$

$x = 14 - 3 y$

$y = \frac{62}{11}$

$x = 14 - 3 y$

$y = \frac{62}{11}$

$x = 14 - 3 y$

Replace all occurrences of $y$ with $\frac{62}{11}$ in each equation.

Replace all occurrences of $y$ in $x = 14 - 3 y$ with $\frac{62}{11}$ .

$x = 14 - 3 (\frac{62}{11})$

$y = \frac{62}{11}$

Simplify the right side.

Simplify $14 - 3 (\frac{62}{11})$ .

Simplify each term.

Multiply $- 3 (\frac{62}{11})$ .

Combine $- 3$ and $\frac{62}{11}$ .

$x = 14 + \frac{- 3 \cdot 62}{11}$

$y = \frac{62}{11}$

Multiply $- 3$ by $62$ .

$x = 14 + \frac{- 186}{11}$

$y = \frac{62}{11}$

$x = 14 + \frac{- 186}{11}$

$y = \frac{62}{11}$

Move the negative in front of the fraction.

$x = 14 - \frac{186}{11}$

$y = \frac{62}{11}$

$x = 14 - \frac{186}{11}$

$y = \frac{62}{11}$

To write $14$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = 14 \cdot \frac{11}{11} - \frac{186}{11}$

$y = \frac{62}{11}$

Combine $14$ and $\frac{11}{11}$ .

$x = \frac{14 \cdot 11}{11} - \frac{186}{11}$

$y = \frac{62}{11}$

Combine the numerators over the common denominator.

$x = \frac{14 \cdot 11 - 186}{11}$

$y = \frac{62}{11}$

Simplify the numerator.

Multiply $14$ by $11$ .

$x = \frac{154 - 186}{11}$

$y = \frac{62}{11}$

Subtract $186$ from $154$ .

$x = \frac{- 32}{11}$

$y = \frac{62}{11}$

$x = \frac{- 32}{11}$

$y = \frac{62}{11}$

Move the negative in front of the fraction.

$x = - \frac{32}{11}$

$y = \frac{62}{11}$

$x = - \frac{32}{11}$

$y = \frac{62}{11}$

$x = - \frac{32}{11}$

$y = \frac{62}{11}$

$x = - \frac{32}{11}$

$y = \frac{62}{11}$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- \frac{32}{11}, \frac{62}{11})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{32}{11}, \frac{62}{11})$

Equation Form:

$x = - \frac{32}{11}, y = \frac{62}{11}$

Solve the System of Equations 14=3y+x , 20=2y-3x

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