Linear Algebra Examples

$2 x - 4 y = 7$

Step 1

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

$- 4 y = 7 - 2 x$

Step 2

Divide each term in $- 4 y = 7 - 2 x$ by $- 4$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $- 4 y = 7 - 2 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{7}{- 4} + \frac{- 2 x}{- 4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{7}{- 4} + \frac{- 2 x}{- 4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{- 4} + \frac{- 2 x}{- 4}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{4} + \frac{- 2 x}{- 4}$

Step 2.3.1.2

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

Tap for more steps...

Step 2.3.1.2.1

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

$y = - \frac{7}{4} + \frac{- 2 (x)}{- 4}$

Step 2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.2.2.1

Factor $- 2$ out of $- 4$ .

$y = - \frac{7}{4} + \frac{- 2 (x)}{- 2 (2)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = - \frac{7}{4} + \frac{- 2 x}{- 2 \cdot 2}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y = - \frac{7}{4} + \frac{x}{2}$

Step 3

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 4