Find the Domain -2x-2y=3x-y

$- 2 x - 2 y = 3 x - y$

Step 1

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

Add $y$ to both sides of the equation.

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

Add $- 2 y$ and $y$ .

$- 2 x - y = 3 x$

Step 2

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

Add $2 x$ to both sides of the equation.

$- y = 3 x + 2 x$

Add $3 x$ and $2 x$ .

$- y = 5 x$

Step 3

Divide each term in $- y = 5 x$ by $- 1$ and simplify.

Divide each term in $- y = 5 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{5 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{5 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{5 x}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{5 x}{- 1}$ .

$y = - 1 \cdot (5 x)$

Rewrite $- 1 \cdot (5 x)$ as $- (5 x)$ .

$y = - (5 x)$

Multiply $5$ by $- 1$ .

$y = - 5 x$

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 -2x-2y=3x-y

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