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

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

Step 1

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

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

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

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

$5 x + 4 y = 3 x$

Step 2

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

Subtract $5 x$ from both sides of the equation.

$4 y = 3 x - 5 x$

Subtract $5 x$ from $3 x$ .

$4 y = - 2 x$

Step 3

Divide each term in $4 y = - 2 x$ by $4$ and simplify.

Divide each term in $4 y = - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{- 2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 2 x}{4}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{4}$

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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 5x-2y=3x-6y

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