Solve the System of Equations -x+2y=14 1/9x-3/4y=-47/18

$- x + 2 y = 14$ $\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Solve for $x$ in $- x + 2 y = 14$ .

Subtract $2 y$ from both sides of the equation.

$- x = 14 - 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Divide each term in $- x = 14 - 2 y$ by $- 1$ and simplify.

Divide each term in $- x = 14 - 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{14}{- 1} + \frac{- 2 y}{- 1}$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{14}{- 1} + \frac{- 2 y}{- 1}$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Divide $x$ by $1$ .

$x = \frac{14}{- 1} + \frac{- 2 y}{- 1}$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

$x = \frac{14}{- 1} + \frac{- 2 y}{- 1}$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Simplify the right side.

Simplify each term.

Divide $14$ by $- 1$ .

$x = - 14 + \frac{- 2 y}{- 1}$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$x = - 14 - 1 \cdot (- 2 y)$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$x = - 14 - (- 2 y)$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Multiply $- 2$ by $- 1$ .

$x = - 14 + 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

$\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$

Replace all occurrences of $x$ with $- 14 + 2 y$ in each equation.

Replace all occurrences of $x$ in $\frac{1}{9} x - \frac{3}{4} y = - \frac{47}{18}$ with $- 14 + 2 y$ .

$\frac{1}{9} \cdot (- 14 + 2 y) - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Simplify the left side.

Simplify $\frac{1}{9} \cdot (- 14 + 2 y) - \frac{3}{4} y$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{9} \cdot - 14 + \frac{1}{9} \cdot (2 y) - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Combine $\frac{1}{9}$ and $- 14$ .

$\frac{- 14}{9} + \frac{1}{9} \cdot (2 y) - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $\frac{1}{9} (2 y)$ .

Combine $2$ and $\frac{1}{9}$ .

$\frac{- 14}{9} + \frac{2}{9} y - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Combine $\frac{2}{9}$ and $y$ .

$\frac{- 14}{9} + \frac{2 y}{9} - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

$\frac{- 14}{9} + \frac{2 y}{9} - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Move the negative in front of the fraction.

$- \frac{14}{9} + \frac{2 y}{9} - \frac{3}{4} y = - \frac{47}{18}$

$x = - 14 + 2 y$

Combine $y$ and $\frac{3}{4}$ .

$- \frac{14}{9} + \frac{2 y}{9} - \frac{y \cdot 3}{4} = - \frac{47}{18}$

$x = - 14 + 2 y$

Move $3$ to the left of $y$ .

$- \frac{14}{9} + \frac{2 y}{9} - \frac{3 y}{4} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} + \frac{2 y}{9} - \frac{3 y}{4} = - \frac{47}{18}$

$x = - 14 + 2 y$

To write $\frac{2 y}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{14}{9} + \frac{2 y}{9} \cdot \frac{4}{4} - \frac{3 y}{4} = - \frac{47}{18}$

$x = - 14 + 2 y$

To write $- \frac{3 y}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{14}{9} + \frac{2 y}{9} \cdot \frac{4}{4} - \frac{3 y}{4} \cdot \frac{9}{9} = - \frac{47}{18}$

$x = - 14 + 2 y$

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 y}{9}$ by $\frac{4}{4}$ .

$- \frac{14}{9} + \frac{2 y \cdot 4}{9 \cdot 4} - \frac{3 y}{4} \cdot \frac{9}{9} = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $9$ by $4$ .

$- \frac{14}{9} + \frac{2 y \cdot 4}{36} - \frac{3 y}{4} \cdot \frac{9}{9} = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $\frac{3 y}{4}$ by $\frac{9}{9}$ .

$- \frac{14}{9} + \frac{2 y \cdot 4}{36} - \frac{3 y \cdot 9}{4 \cdot 9} = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $4$ by $9$ .

$- \frac{14}{9} + \frac{2 y \cdot 4}{36} - \frac{3 y \cdot 9}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} + \frac{2 y \cdot 4}{36} - \frac{3 y \cdot 9}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Combine the numerators over the common denominator.

$- \frac{14}{9} + \frac{2 y \cdot 4 - 3 y \cdot 9}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $2 y \cdot 4 - 3 y \cdot 9$ .

Factor $y$ out of $2 y \cdot 4$ .

$- \frac{14}{9} + \frac{y (2 \cdot 4) - 3 y \cdot 9}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Factor $y$ out of $- 3 y \cdot 9$ .

$- \frac{14}{9} + \frac{y (2 \cdot 4) + y (- 3 \cdot 9)}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Factor $y$ out of $y (2 \cdot 4) + y (- 3 \cdot 9)$ .

$- \frac{14}{9} + \frac{y (2 \cdot 4 - 3 \cdot 9)}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} + \frac{y (2 \cdot 4 - 3 \cdot 9)}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $2$ by $4$ .

$- \frac{14}{9} + \frac{y (8 - 3 \cdot 9)}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Multiply $- 3$ by $9$ .

$- \frac{14}{9} + \frac{y (8 - 27)}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Subtract $27$ from $8$ .

$- \frac{14}{9} + \frac{y \cdot - 19}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} + \frac{y \cdot - 19}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Move $- 19$ to the left of $y$ .

$- \frac{14}{9} + \frac{- 19 \cdot y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Move the negative in front of the fraction.

$- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

$- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$

$x = - 14 + 2 y$

Solve for $y$ in $- \frac{14}{9} - \frac{19 y}{36} = - \frac{47}{18}$ .

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

Add $\frac{14}{9}$ to both sides of the equation.

$- \frac{19 y}{36} = - \frac{47}{18} + \frac{14}{9}$

$x = - 14 + 2 y$

To write $\frac{14}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{19 y}{36} = - \frac{47}{18} + \frac{14}{9} \cdot \frac{2}{2}$

$x = - 14 + 2 y$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{14}{9}$ by $\frac{2}{2}$ .

$- \frac{19 y}{36} = - \frac{47}{18} + \frac{14 \cdot 2}{9 \cdot 2}$

$x = - 14 + 2 y$

Multiply $9$ by $2$ .

$- \frac{19 y}{36} = - \frac{47}{18} + \frac{14 \cdot 2}{18}$

$x = - 14 + 2 y$

$- \frac{19 y}{36} = - \frac{47}{18} + \frac{14 \cdot 2}{18}$

$x = - 14 + 2 y$

Combine the numerators over the common denominator.

$- \frac{19 y}{36} = \frac{- 47 + 14 \cdot 2}{18}$

$x = - 14 + 2 y$

Simplify the numerator.

Multiply $14$ by $2$ .

$- \frac{19 y}{36} = \frac{- 47 + 28}{18}$

$x = - 14 + 2 y$

Add $- 47$ and $28$ .

$- \frac{19 y}{36} = \frac{- 19}{18}$

$x = - 14 + 2 y$

$- \frac{19 y}{36} = \frac{- 19}{18}$

$x = - 14 + 2 y$

Move the negative in front of the fraction.

$- \frac{19 y}{36} = - \frac{19}{18}$

$x = - 14 + 2 y$

$- \frac{19 y}{36} = - \frac{19}{18}$

$x = - 14 + 2 y$

Multiply both sides of the equation by $- \frac{36}{19}$ .

$- \frac{36}{19} \cdot (- \frac{19 y}{36}) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{36}{19} (- \frac{19 y}{36})$ .

Cancel the common factor of $36$ .

Move the leading negative in $- \frac{36}{19}$ into the numerator.

$\frac{- 36}{19} \cdot (- \frac{19 y}{36}) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Move the leading negative in $- \frac{19 y}{36}$ into the numerator.

$\frac{- 36}{19} \cdot \frac{- 19 y}{36} = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Factor $36$ out of $- 36$ .

$\frac{36 (- 1)}{19} \cdot \frac{- 19 y}{36} = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Cancel the common factor.

$\frac{36 \cdot - 1}{19} \cdot \frac{- 19 y}{36} = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Rewrite the expression.

$\frac{- 1}{19} \cdot (- 19 y) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

$\frac{- 1}{19} \cdot (- 19 y) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Cancel the common factor of $19$ .

Factor $19$ out of $- 19 y$ .

$\frac{- 1}{19} \cdot (19 (- y)) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Cancel the common factor.

$\frac{- 1}{19} \cdot (19 (- y)) = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Rewrite the expression.

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Multiply $y$ by $1$ .

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

$y = - \frac{36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Simplify the right side.

Simplify $- \frac{36}{19} (- \frac{19}{18})$ .

Cancel the common factor of $18$ .

Move the leading negative in $- \frac{36}{19}$ into the numerator.

$y = \frac{- 36}{19} \cdot (- \frac{19}{18})$

$x = - 14 + 2 y$

Move the leading negative in $- \frac{19}{18}$ into the numerator.

$y = \frac{- 36}{19} \cdot \frac{- 19}{18}$

$x = - 14 + 2 y$

Factor $18$ out of $- 36$ .

$y = \frac{18 (- 2)}{19} \cdot \frac{- 19}{18}$

$x = - 14 + 2 y$

Cancel the common factor.

$y = \frac{18 \cdot - 2}{19} \cdot \frac{- 19}{18}$

$x = - 14 + 2 y$

Rewrite the expression.

$y = \frac{- 2}{19} \cdot - 19$

$x = - 14 + 2 y$

$y = \frac{- 2}{19} \cdot - 19$

$x = - 14 + 2 y$

Cancel the common factor of $19$ .

Factor $19$ out of $- 19$ .

$y = \frac{- 2}{19} \cdot (19 (- 1))$

$x = - 14 + 2 y$

Cancel the common factor.

$y = \frac{- 2}{19} \cdot (19 \cdot - 1)$

$x = - 14 + 2 y$

Rewrite the expression.

$y = - 2 \cdot - 1$

$x = - 14 + 2 y$

$y = - 2 \cdot - 1$

$x = - 14 + 2 y$

Multiply $- 2$ by $- 1$ .

$y = 2$

$x = - 14 + 2 y$

$y = 2$

$x = - 14 + 2 y$

$y = 2$

$x = - 14 + 2 y$

$y = 2$

$x = - 14 + 2 y$

$y = 2$

$x = - 14 + 2 y$

Replace all occurrences of $y$ with $2$ in each equation.

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

$x = - 14 + 2 (2)$

$y = 2$

Simplify the right side.

Simplify $- 14 + 2 (2)$ .

Multiply $2$ by $2$ .

$x = - 14 + 4$

$y = 2$

Add $- 14$ and $4$ .

$x = - 10$

$y = 2$

$x = - 10$

$y = 2$

$x = - 10$

$y = 2$

$x = - 10$

$y = 2$

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

$(- 10, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 10, 2)$

Equation Form:

$x = - 10, y = 2$

Solve the System of Equations -x+2y=14 1/9x-3/4y=-47/18

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