Solve the System of Equations -2x-y=-5 and 5x+6y=-19

$- 2 x - y = - 5$ and $5 x + 6 y = - 19$

Solve for $x$ in $- 2 x - y = - 5$ .

Add $y$ to both sides of the equation.

$- 2 x = - 5 + y$

$5 x + 6 y = - 19$

Divide each term in $- 2 x = - 5 + y$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 5 + y$ by $- 2$ .

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

$5 x + 6 y = - 19$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$5 x + 6 y = - 19$

Divide $x$ by $1$ .

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

$5 x + 6 y = - 19$

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

$5 x + 6 y = - 19$

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

$5 x + 6 y = - 19$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

$5 x + 6 y = - 19$

Move the negative in front of the fraction.

$x = \frac{5}{2} - \frac{y}{2}$

$5 x + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$5 x + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$5 x + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$5 x + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$5 x + 6 y = - 19$

Replace all occurrences of $x$ with $\frac{5}{2} - \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $5 x + 6 y = - 19$ with $\frac{5}{2} - \frac{y}{2}$ .

$5 (\frac{5}{2} - \frac{y}{2}) + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Simplify the left side.

Simplify $5 (\frac{5}{2} - \frac{y}{2}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$5 (\frac{5}{2}) + 5 (- \frac{y}{2}) + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Multiply $5 (\frac{5}{2})$ .

Combine $5$ and $\frac{5}{2}$ .

$\frac{5 \cdot 5}{2} + 5 (- \frac{y}{2}) + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Multiply $5$ by $5$ .

$\frac{25}{2} + 5 (- \frac{y}{2}) + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25}{2} + 5 (- \frac{y}{2}) + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Multiply $5 (- \frac{y}{2})$ .

Multiply $- 1$ by $5$ .

$\frac{25}{2} - 5 \frac{y}{2} + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Combine $- 5$ and $\frac{y}{2}$ .

$\frac{25}{2} + \frac{- 5 y}{2} + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25}{2} + \frac{- 5 y}{2} + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Move the negative in front of the fraction.

$\frac{25}{2} - \frac{5 y}{2} + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25}{2} - \frac{5 y}{2} + 6 y = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{2} - \frac{5 y}{2} + 6 y \cdot \frac{2}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Combine $6 y$ and $\frac{2}{2}$ .

$\frac{25}{2} - \frac{5 y}{2} + \frac{6 y \cdot 2}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$\frac{25}{2} + \frac{- 5 y + 6 y \cdot 2}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$\frac{25 - 5 y + 6 y \cdot 2}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Multiply $2$ by $6$ .

$\frac{25 - 5 y + 12 y}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Add $- 5 y$ and $12 y$ .

$\frac{25 + 7 y}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25 + 7 y}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25 + 7 y}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

$\frac{25 + 7 y}{2} = - 19$

$x = \frac{5}{2} - \frac{y}{2}$

Solve for $y$ in $\frac{25 + 7 y}{2} = - 19$ .

Multiply both sides by $2$ .

$\frac{25 + 7 y}{2} \cdot 2 = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

Simplify.

Simplify the left side.

Simplify $\frac{25 + 7 y}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{25 + 7 y}{2} \cdot 2 = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

Rewrite the expression.

$25 + 7 y = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

$25 + 7 y = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

Reorder $25$ and $7 y$ .

$7 y + 25 = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

$7 y + 25 = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

$7 y + 25 = - 19 \cdot 2$

$x = \frac{5}{2} - \frac{y}{2}$

Simplify the right side.

Multiply $- 19$ by $2$ .

$7 y + 25 = - 38$

$x = \frac{5}{2} - \frac{y}{2}$

$7 y + 25 = - 38$

$x = \frac{5}{2} - \frac{y}{2}$

$7 y + 25 = - 38$

$x = \frac{5}{2} - \frac{y}{2}$

Solve for $y$ .

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

Subtract $25$ from both sides of the equation.

$7 y = - 38 - 25$

$x = \frac{5}{2} - \frac{y}{2}$

Subtract $25$ from $- 38$ .

$7 y = - 63$

$x = \frac{5}{2} - \frac{y}{2}$

$7 y = - 63$

$x = \frac{5}{2} - \frac{y}{2}$

Divide each term in $7 y = - 63$ by $7$ and simplify.

Divide each term in $7 y = - 63$ by $7$ .

$\frac{7 y}{7} = \frac{- 63}{7}$

$x = \frac{5}{2} - \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 63}{7}$

$x = \frac{5}{2} - \frac{y}{2}$

Divide $y$ by $1$ .

$y = \frac{- 63}{7}$

$x = \frac{5}{2} - \frac{y}{2}$

$y = \frac{- 63}{7}$

$x = \frac{5}{2} - \frac{y}{2}$

$y = \frac{- 63}{7}$

$x = \frac{5}{2} - \frac{y}{2}$

Simplify the right side.

Divide $- 63$ by $7$ .

$y = - 9$

$x = \frac{5}{2} - \frac{y}{2}$

$y = - 9$

$x = \frac{5}{2} - \frac{y}{2}$

$y = - 9$

$x = \frac{5}{2} - \frac{y}{2}$

$y = - 9$

$x = \frac{5}{2} - \frac{y}{2}$

$y = - 9$

$x = \frac{5}{2} - \frac{y}{2}$

Replace all occurrences of $y$ with $- 9$ in each equation.

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

$x = \frac{5}{2} - \frac{- 9}{2}$

$y = - 9$

Simplify the right side.

Simplify $\frac{5}{2} - \frac{- 9}{2}$ .

Combine the numerators over the common denominator.

$x = \frac{5 + 9}{2}$

$y = - 9$

Simplify the expression.

Add $5$ and $9$ .

$x = \frac{14}{2}$

$y = - 9$

Divide $14$ by $2$ .

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

$x = 7$

$y = - 9$

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

$(7, - 9)$

The result can be shown in multiple forms.

Point Form:

$(7, - 9)$

Equation Form:

$x = 7, y = - 9$

Solve the System of Equations -2x-y=-5 and 5x+6y=-19

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