Find the Domain -6x-5y=2x+3y

$- 6 x - 5 y = 2 x + 3 y$

Step 1

Move all terms containing $y$ to the left side of the equation.

Subtract $3 y$ from both sides of the equation.

$- 6 x - 5 y - 3 y = 2 x$

Subtract $3 y$ from $- 5 y$ .

$- 6 x - 8 y = 2 x$

Step 2

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

Add $6 x$ to both sides of the equation.

$- 8 y = 2 x + 6 x$

Add $2 x$ and $6 x$ .

$- 8 y = 8 x$

Step 3

Divide each term in $- 8 y = 8 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 8 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{8 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{8 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{8 x}{- 8}$

Simplify the right side.

Cancel the common factor of $8$ and $- 8$ .

Factor $8$ out of $8 x$ .

$y = \frac{8 (x)}{- 8}$

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

$y = - 1 \cdot x$

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

$y = - x$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5

Find the Domain -6x-5y=2x+3y

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