Solve the System of Equations -x-y=3 and 6x+2y=-30

$- x - y = 3$ and $6 x + 2 y = - 30$

Step 1

Solve for $x$ in $- x - y = 3$ .

Add $y$ to both sides of the equation.

$- x = 3 + y$

$6 x + 2 y = - 30$

Divide each term in $- x = 3 + y$ by $- 1$ and simplify.

Divide each term in $- x = 3 + y$ by $- 1$ .

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

$6 x + 2 y = - 30$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$6 x + 2 y = - 30$

Divide $x$ by $1$ .

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

$6 x + 2 y = - 30$

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

$6 x + 2 y = - 30$

Simplify the right side.

Simplify each term.

Divide $3$ by $- 1$ .

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

$6 x + 2 y = - 30$

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

$x = - 3 - 1 \cdot y$

$6 x + 2 y = - 30$

Rewrite $- 1 \cdot y$ as $- y$ .

$x = - 3 - y$

$6 x + 2 y = - 30$

$x = - 3 - y$

$6 x + 2 y = - 30$

$x = - 3 - y$

$6 x + 2 y = - 30$

$x = - 3 - y$

$6 x + 2 y = - 30$

$x = - 3 - y$

$6 x + 2 y = - 30$

Step 2

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

Replace all occurrences of $x$ in $6 x + 2 y = - 30$ with $- 3 - y$ .

$6 (- 3 - y) + 2 y = - 30$

$x = - 3 - y$

Simplify the left side.

Simplify $6 (- 3 - y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$6 \cdot - 3 + 6 (- y) + 2 y = - 30$

$x = - 3 - y$

Multiply $6$ by $- 3$ .

$- 18 + 6 (- y) + 2 y = - 30$

$x = - 3 - y$

Multiply $- 1$ by $6$ .

$- 18 - 6 y + 2 y = - 30$

$x = - 3 - y$

$- 18 - 6 y + 2 y = - 30$

$x = - 3 - y$

Add $- 6 y$ and $2 y$ .

$- 18 - 4 y = - 30$

$x = - 3 - y$

$- 18 - 4 y = - 30$

$x = - 3 - y$

$- 18 - 4 y = - 30$

$x = - 3 - y$

$- 18 - 4 y = - 30$

$x = - 3 - y$

Step 3

Solve for $y$ in $- 18 - 4 y = - 30$ .

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

Add $18$ to both sides of the equation.

$- 4 y = - 30 + 18$

$x = - 3 - y$

Add $- 30$ and $18$ .

$- 4 y = - 12$

$x = - 3 - y$

$- 4 y = - 12$

$x = - 3 - y$

Divide each term in $- 4 y = - 12$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 12$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 12}{- 4}$

$x = - 3 - y$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 12}{- 4}$

$x = - 3 - y$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 4}$

$x = - 3 - y$

$y = \frac{- 12}{- 4}$

$x = - 3 - y$

$y = \frac{- 12}{- 4}$

$x = - 3 - y$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$y = 3$

$x = - 3 - y$

$y = 3$

$x = - 3 - y$

$y = 3$

$x = - 3 - y$

$y = 3$

$x = - 3 - y$

Step 4

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

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

$x = - 3 - (3)$

$y = 3$

Simplify the right side.

Simplify $- 3 - (3)$ .

Multiply $- 1$ by $3$ .

$x = - 3 - 3$

$y = 3$

Subtract $3$ from $- 3$ .

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

Step 5

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

$(- 6, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 3)$

Equation Form:

$x = - 6, y = 3$

Step 7

Solve the System of Equations -x-y=3 and 6x+2y=-30

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