Linear Algebra Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

$x y = y \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move $2$ to the left of $y$ .

$x y = 2 y$

Step 3

Solve for $y$ .

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Step 3.1

Subtract $2 y$ from both sides of the equation.

$x y - 2 y = 0$

Step 3.2

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

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Step 3.2.1

Factor $y$ out of $x y$ .

$y x - 2 y = 0$

Step 3.2.2

Factor $y$ out of $- 2 y$ .

$y x + y \cdot - 2 = 0$

Step 3.2.3

Factor $y$ out of $y x + y \cdot - 2$ .

$y (x - 2) = 0$

Step 3.3

Divide each term in $y (x - 2) = 0$ by $x - 2$ and simplify.

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Step 3.3.1

Divide each term in $y (x - 2) = 0$ by $x - 2$ .

$\frac{y (x - 2)}{x - 2} = \frac{0}{x - 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $x - 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{y (x - 2)}{x - 2} = \frac{0}{x - 2}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{x - 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $0$ by $x - 2$ .

$y = 0$

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