Find the Domain -2x-5y=4x-y

$- 2 x - 5 y = 4 x - y$

Step 1

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

Add $y$ to both sides of the equation.

$- 2 x - 5 y + y = 4 x$

Add $- 5 y$ and $y$ .

$- 2 x - 4 y = 4 x$

Step 2

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

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

$- 4 y = 4 x + 2 x$

Add $4 x$ and $2 x$ .

$- 4 y = 6 x$

Step 3

Divide each term in $- 4 y = 6 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 6 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{6 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{6 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{6 x}{- 4}$

Simplify the right side.

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 (3 x)}{2 (- 2)}$

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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-5y=4x-y

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