Solve the System of Equations -1/2x+1/5y=9 7x+1/3y=-2/3

$- \frac{1}{2} x + \frac{1}{5} y = 9$ $7 x + \frac{1}{3} y = - \frac{2}{3}$

Solve for $x$ in $7 x + \frac{1}{3} y = - \frac{2}{3}$ .

Combine $\frac{1}{3}$ and $y$ .

$7 x + \frac{y}{3} = - \frac{2}{3}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Subtract $\frac{y}{3}$ from both sides of the equation.

$7 x = - \frac{2}{3} - \frac{y}{3}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Divide each term in $7 x = - \frac{2}{3} - \frac{y}{3}$ by $7$ and simplify.

Divide each term in $7 x = - \frac{2}{3} - \frac{y}{3}$ by $7$ .

$\frac{7 x}{7} = \frac{- \frac{2}{3}}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- \frac{2}{3}}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Divide $x$ by $1$ .

$x = \frac{- \frac{2}{3}}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = \frac{- \frac{2}{3}}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = \frac{- \frac{2}{3}}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{2}{3} \cdot \frac{1}{7} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Multiply $- \frac{2}{3} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{2}{3}$ .

$x = - \frac{2}{7 \cdot 3} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Multiply $7$ by $3$ .

$x = - \frac{2}{21} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} + \frac{- \frac{y}{3}}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{2}{21} - \frac{y}{3} \cdot \frac{1}{7}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Multiply $- \frac{y}{3} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{y}{3}$ .

$x = - \frac{2}{21} - \frac{y}{7 \cdot 3}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Multiply $7$ by $3$ .

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- \frac{1}{2} x + \frac{1}{5} y = 9$

Replace all occurrences of $x$ with $- \frac{2}{21} - \frac{y}{21}$ in each equation.

Replace all occurrences of $x$ in $- \frac{1}{2} x + \frac{1}{5} y = 9$ with $- \frac{2}{21} - \frac{y}{21}$ .

$- \frac{1}{2} \cdot (- \frac{2}{21} - \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Simplify the left side.

Simplify $- \frac{1}{2} \cdot (- \frac{2}{21} - \frac{y}{21}) + \frac{1}{5} y$ .

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} \cdot (- \frac{2}{21}) - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot (- \frac{2}{21}) - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Move the leading negative in $- \frac{2}{21}$ into the numerator.

$\frac{- 1}{2} \cdot \frac{- 2}{21} - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Factor $2$ out of $- 2$ .

$\frac{- 1}{2} \cdot \frac{2 (- 1)}{21} - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor.

$\frac{- 1}{2} \cdot \frac{2 \cdot - 1}{21} - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Rewrite the expression.

$- 1 (\frac{- 1}{21}) - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- 1 (\frac{- 1}{21}) - \frac{1}{2} \cdot (- \frac{y}{21}) + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $- \frac{1}{2} (- \frac{y}{21})$ .

Multiply $- 1$ by $- 1$ .

$- 1 (\frac{- 1}{21}) + 1 (\frac{1}{2}) \cdot \frac{y}{21} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $\frac{1}{2}$ by $1$ .

$- 1 (\frac{- 1}{21}) + \frac{1}{2} \cdot \frac{y}{21} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $\frac{1}{2}$ by $\frac{y}{21}$ .

$- 1 (\frac{- 1}{21}) + \frac{y}{2 \cdot 21} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $2$ by $21$ .

$- 1 (\frac{- 1}{21}) + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$- 1 (\frac{- 1}{21}) + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Simplify each term.

Move the negative in front of the fraction.

$- 1 (- \frac{1}{21}) + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $- 1 (- \frac{1}{21})$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{21}) + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $\frac{1}{21}$ by $1$ .

$\frac{1}{21} + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{y}{42} + \frac{1}{5} y = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Combine $\frac{1}{5}$ and $y$ .

$\frac{1}{21} + \frac{y}{42} + \frac{y}{5} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{y}{42} + \frac{y}{5} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

To write $\frac{y}{42}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{21} + \frac{y}{42} \cdot \frac{5}{5} + \frac{y}{5} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{42}{42}$ .

$\frac{1}{21} + \frac{y}{42} \cdot \frac{5}{5} + \frac{y}{5} \cdot \frac{42}{42} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Write each expression with a common denominator of $210$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{42}$ by $\frac{5}{5}$ .

$\frac{1}{21} + \frac{y \cdot 5}{42 \cdot 5} + \frac{y}{5} \cdot \frac{42}{42} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $42$ by $5$ .

$\frac{1}{21} + \frac{y \cdot 5}{210} + \frac{y}{5} \cdot \frac{42}{42} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $\frac{y}{5}$ by $\frac{42}{42}$ .

$\frac{1}{21} + \frac{y \cdot 5}{210} + \frac{y \cdot 42}{5 \cdot 42} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $5$ by $42$ .

$\frac{1}{21} + \frac{y \cdot 5}{210} + \frac{y \cdot 42}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{y \cdot 5}{210} + \frac{y \cdot 42}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Combine the numerators over the common denominator.

$\frac{1}{21} + \frac{y \cdot 5 + y \cdot 42}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Reorder $y$ and $42$ .

$\frac{1}{21} + \frac{5 \cdot y + 42 \cdot y}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Add $5 \cdot y$ and $42 \cdot y$ .

$\frac{1}{21} + \frac{47 y}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{47 y}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{47 y}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{21} + \frac{47 y}{210} = 9$

$x = - \frac{2}{21} - \frac{y}{21}$

Solve for $y$ in $\frac{1}{21} + \frac{47 y}{210} = 9$ .

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

Subtract $\frac{1}{21}$ from both sides of the equation.

$\frac{47 y}{210} = 9 - \frac{1}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{21}{21}$ .

$\frac{47 y}{210} = 9 \cdot \frac{21}{21} - \frac{1}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Combine $9$ and $\frac{21}{21}$ .

$\frac{47 y}{210} = \frac{9 \cdot 21}{21} - \frac{1}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Combine the numerators over the common denominator.

$\frac{47 y}{210} = \frac{9 \cdot 21 - 1}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Simplify the numerator.

Multiply $9$ by $21$ .

$\frac{47 y}{210} = \frac{189 - 1}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Subtract $1$ from $189$ .

$\frac{47 y}{210} = \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{47 y}{210} = \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{47 y}{210} = \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply both sides of the equation by $\frac{210}{47}$ .

$\frac{210}{47} \cdot \frac{47 y}{210} = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{210}{47} \cdot \frac{47 y}{210}$ .

Cancel the common factor of $210$ .

Cancel the common factor.

$\frac{210}{47} \cdot \frac{47 y}{210} = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Rewrite the expression.

$\frac{1}{47} \cdot (47 y) = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$\frac{1}{47} \cdot (47 y) = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor of $47$ .

Factor $47$ out of $47 y$ .

$\frac{1}{47} \cdot (47 (y)) = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor.

$\frac{1}{47} \cdot (47 y) = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Rewrite the expression.

$y = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = \frac{210}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Simplify the right side.

Simplify $\frac{210}{47} \cdot \frac{188}{21}$ .

Cancel the common factor of $21$ .

Factor $21$ out of $210$ .

$y = \frac{21 (10)}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor.

$y = \frac{21 \cdot 10}{47} \cdot \frac{188}{21}$

$x = - \frac{2}{21} - \frac{y}{21}$

Rewrite the expression.

$y = \frac{10}{47} \cdot 188$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = \frac{10}{47} \cdot 188$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor of $47$ .

Factor $47$ out of $188$ .

$y = \frac{10}{47} \cdot (47 (4))$

$x = - \frac{2}{21} - \frac{y}{21}$

Cancel the common factor.

$y = \frac{10}{47} \cdot (47 \cdot 4)$

$x = - \frac{2}{21} - \frac{y}{21}$

Rewrite the expression.

$y = 10 \cdot 4$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = 10 \cdot 4$

$x = - \frac{2}{21} - \frac{y}{21}$

Multiply $10$ by $4$ .

$y = 40$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = 40$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = 40$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = 40$

$x = - \frac{2}{21} - \frac{y}{21}$

$y = 40$

$x = - \frac{2}{21} - \frac{y}{21}$

Replace all occurrences of $y$ with $40$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{2}{21} - \frac{y}{21}$ with $40$ .

$x = - \frac{2}{21} - \frac{40}{21}$

$y = 40$

Simplify the right side.

Simplify $- \frac{2}{21} - \frac{40}{21}$ .

Combine the numerators over the common denominator.

$x = \frac{- 2 - 40}{21}$

$y = 40$

Simplify the expression.

Subtract $40$ from $- 2$ .

$x = \frac{- 42}{21}$

$y = 40$

Divide $- 42$ by $21$ .

$x = - 2$

$y = 40$

$x = - 2$

$y = 40$

$x = - 2$

$y = 40$

$x = - 2$

$y = 40$

$x = - 2$

$y = 40$

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

$(- 2, 40)$

The result can be shown in multiple forms.

Point Form:

$(- 2, 40)$

Equation Form:

$x = - 2, y = 40$

Solve the System of Equations -1/2x+1/5y=9 7x+1/3y=-2/3

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