Solve the System of Equations -4/5x+7y=-1/5 1/2x-1/3y=-12

$- \frac{4}{5} x + 7 y = - \frac{1}{5}$ $\frac{1}{2} x - \frac{1}{3} y = - 12$

Solve for $y$ in $- \frac{4}{5} x + 7 y = - \frac{1}{5}$ .

Simplify each term.

Combine $x$ and $\frac{4}{5}$ .

$- \frac{x \cdot 4}{5} + 7 y = - \frac{1}{5}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Move $4$ to the left of $x$ .

$- \frac{4 x}{5} + 7 y = - \frac{1}{5}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$- \frac{4 x}{5} + 7 y = - \frac{1}{5}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Add $\frac{4 x}{5}$ to both sides of the equation.

$7 y = - \frac{1}{5} + \frac{4 x}{5}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Divide each term in $7 y = - \frac{1}{5} + \frac{4 x}{5}$ by $7$ and simplify.

Divide each term in $7 y = - \frac{1}{5} + \frac{4 x}{5}$ by $7$ .

$\frac{7 y}{7} = \frac{- \frac{1}{5}}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- \frac{1}{5}}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Divide $y$ by $1$ .

$y = \frac{- \frac{1}{5}}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = \frac{- \frac{1}{5}}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = \frac{- \frac{1}{5}}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{1}{5} \cdot \frac{1}{7} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Multiply $- \frac{1}{5} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{1}{5}$ .

$y = - \frac{1}{7 \cdot 5} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Multiply $7$ by $5$ .

$y = - \frac{1}{35} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{\frac{4 x}{5}}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{1}{35} + \frac{4 x}{5} \cdot \frac{1}{7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Multiply $\frac{4 x}{5} \cdot \frac{1}{7}$ .

Multiply $\frac{4 x}{5}$ by $\frac{1}{7}$ .

$y = - \frac{1}{35} + \frac{4 x}{5 \cdot 7}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Multiply $5$ by $7$ .

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{2} x - \frac{1}{3} y = - 12$

Replace all occurrences of $y$ with $- \frac{1}{35} + \frac{4 x}{35}$ in each equation.

Replace all occurrences of $y$ in $\frac{1}{2} x - \frac{1}{3} y = - 12$ with $- \frac{1}{35} + \frac{4 x}{35}$ .

$\frac{1}{2} x - \frac{1}{3} \cdot (- \frac{1}{35} + \frac{4 x}{35}) = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Simplify the left side.

Simplify $\frac{1}{2} x - \frac{1}{3} \cdot (- \frac{1}{35} + \frac{4 x}{35})$ .

Simplify each term.

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

$\frac{x}{2} - \frac{1}{3} \cdot (- \frac{1}{35} + \frac{4 x}{35}) = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Apply the distributive property.

$\frac{x}{2} - \frac{1}{3} \cdot (- \frac{1}{35}) - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $- \frac{1}{3} (- \frac{1}{35})$ .

Multiply $- 1$ by $- 1$ .

$\frac{x}{2} + 1 (\frac{1}{3}) \cdot \frac{1}{35} - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

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

$\frac{x}{2} + \frac{1}{3} \cdot \frac{1}{35} - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $\frac{1}{3}$ by $\frac{1}{35}$ .

$\frac{x}{2} + \frac{1}{3 \cdot 35} - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $3$ by $35$ .

$\frac{x}{2} + \frac{1}{105} - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x}{2} + \frac{1}{105} - \frac{1}{3} \cdot \frac{4 x}{35} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $- \frac{1}{3} \cdot \frac{4 x}{35}$ .

Multiply $\frac{4 x}{35}$ by $\frac{1}{3}$ .

$\frac{x}{2} + \frac{1}{105} - \frac{4 x}{35 \cdot 3} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $35$ by $3$ .

$\frac{x}{2} + \frac{1}{105} - \frac{4 x}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x}{2} + \frac{1}{105} - \frac{4 x}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x}{2} + \frac{1}{105} - \frac{4 x}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{105}{105}$ .

$\frac{x}{2} \cdot \frac{105}{105} - \frac{4 x}{105} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

To write $- \frac{4 x}{105}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} \cdot \frac{105}{105} - \frac{4 x}{105} \cdot \frac{2}{2} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

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

Multiply $\frac{x}{2}$ by $\frac{105}{105}$ .

$\frac{x \cdot 105}{2 \cdot 105} - \frac{4 x}{105} \cdot \frac{2}{2} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $2$ by $105$ .

$\frac{x \cdot 105}{210} - \frac{4 x}{105} \cdot \frac{2}{2} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $\frac{4 x}{105}$ by $\frac{2}{2}$ .

$\frac{x \cdot 105}{210} - \frac{4 x \cdot 2}{105 \cdot 2} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $105$ by $2$ .

$\frac{x \cdot 105}{210} - \frac{4 x \cdot 2}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x \cdot 105}{210} - \frac{4 x \cdot 2}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Combine the numerators over the common denominator.

$\frac{x \cdot 105 - 4 x \cdot 2}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 105 - 4 x \cdot 2$ .

Factor $x$ out of $x \cdot 105$ .

$\frac{x (105) - 4 x \cdot 2}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Factor $x$ out of $- 4 x \cdot 2$ .

$\frac{x (105) + x (- 4 \cdot 2)}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Factor $x$ out of $x (105) + x (- 4 \cdot 2)$ .

$\frac{x (105 - 4 \cdot 2)}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x (105 - 4 \cdot 2)}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $- 4$ by $2$ .

$\frac{x (105 - 8)}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Subtract $8$ from $105$ .

$\frac{x \cdot 97}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{x \cdot 97}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Move $97$ to the left of $x$ .

$\frac{97 x}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} + \frac{1}{105} = - 12$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Solve for $x$ in $\frac{97 x}{210} + \frac{1}{105} = - 12$ .

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

Subtract $\frac{1}{105}$ from both sides of the equation.

$\frac{97 x}{210} = - 12 - \frac{1}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

To write $- 12$ as a fraction with a common denominator, multiply by $\frac{105}{105}$ .

$\frac{97 x}{210} = - 12 \cdot \frac{105}{105} - \frac{1}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Combine $- 12$ and $\frac{105}{105}$ .

$\frac{97 x}{210} = \frac{- 12 \cdot 105}{105} - \frac{1}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Combine the numerators over the common denominator.

$\frac{97 x}{210} = \frac{- 12 \cdot 105 - 1}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Simplify the numerator.

Multiply $- 12$ by $105$ .

$\frac{97 x}{210} = \frac{- 1260 - 1}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Subtract $1$ from $- 1260$ .

$\frac{97 x}{210} = \frac{- 1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} = \frac{- 1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Move the negative in front of the fraction.

$\frac{97 x}{210} = - \frac{1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{97 x}{210} = - \frac{1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply both sides of the equation by $\frac{210}{97}$ .

$\frac{210}{97} \cdot \frac{97 x}{210} = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{210}{97} \cdot \frac{97 x}{210}$ .

Cancel the common factor of $210$ .

Cancel the common factor.

$\frac{210}{97} \cdot \frac{97 x}{210} = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Rewrite the expression.

$\frac{1}{97} \cdot (97 x) = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$\frac{1}{97} \cdot (97 x) = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Cancel the common factor of $97$ .

Factor $97$ out of $97 x$ .

$\frac{1}{97} \cdot (97 (x)) = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Cancel the common factor.

$\frac{1}{97} \cdot (97 x) = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Rewrite the expression.

$x = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = \frac{210}{97} \cdot (- \frac{1261}{105})$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Simplify the right side.

Simplify $\frac{210}{97} (- \frac{1261}{105})$ .

Cancel the common factor of $105$ .

Move the leading negative in $- \frac{1261}{105}$ into the numerator.

$x = \frac{210}{97} \cdot \frac{- 1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Factor $105$ out of $210$ .

$x = \frac{105 (2)}{97} \cdot \frac{- 1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Cancel the common factor.

$x = \frac{105 \cdot 2}{97} \cdot \frac{- 1261}{105}$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Rewrite the expression.

$x = \frac{2}{97} \cdot - 1261$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = \frac{2}{97} \cdot - 1261$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Cancel the common factor of $97$ .

Factor $97$ out of $- 1261$ .

$x = \frac{2}{97} \cdot (97 (- 13))$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Cancel the common factor.

$x = \frac{2}{97} \cdot (97 \cdot - 13)$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Rewrite the expression.

$x = 2 \cdot - 13$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = 2 \cdot - 13$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Multiply $2$ by $- 13$ .

$x = - 26$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = - 26$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = - 26$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = - 26$

$y = - \frac{1}{35} + \frac{4 x}{35}$

$x = - 26$

$y = - \frac{1}{35} + \frac{4 x}{35}$

Replace all occurrences of $x$ with $- 26$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{1}{35} + \frac{4 x}{35}$ with $- 26$ .

$y = - \frac{1}{35} + \frac{4 (- 26)}{35}$

$x = - 26$

Simplify the right side.

Simplify $- \frac{1}{35} + \frac{4 (- 26)}{35}$ .

Combine the numerators over the common denominator.

$y = \frac{- 1 + 4 (- 26)}{35}$

$x = - 26$

Simplify the expression.

Multiply $4$ by $- 26$ .

$y = \frac{- 1 - 104}{35}$

$x = - 26$

Subtract $104$ from $- 1$ .

$y = \frac{- 105}{35}$

$x = - 26$

Divide $- 105$ by $35$ .

$y = - 3$

$x = - 26$

$y = - 3$

$x = - 26$

$y = - 3$

$x = - 26$

$y = - 3$

$x = - 26$

$y = - 3$

$x = - 26$

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

$(- 26, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 26, - 3)$

Equation Form:

$x = - 26, y = - 3$

Solve the System of Equations -4/5x+7y=-1/5 1/2x-1/3y=-12

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