Finite Math Examples

$2 x - y = 2$ , $5 x + 6 y + 9$

Step 1

Add $y$ to both sides of the equation.

$2 x = 2 + y$

Step 2

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

Tap for more steps...

Step 2.1

Divide each term in $2 x = 2 + y$ by $2$ .

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $2$ by $2$ .

$x = 1 + \frac{y}{2}$

Step 3

Replace the variable $x$ with $1 + \frac{y}{2}$ in the expression.

$5 (1 + \frac{y}{2}) + 6 y + 9$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

$5 \cdot 1 + 5 \frac{y}{2} + 6 y + 9$

Step 4.2

Multiply $5$ by $1$ .

$5 + 5 \frac{y}{2} + 6 y + 9$

Step 4.3

Combine $5$ and $\frac{y}{2}$ .

$5 + \frac{5 y}{2} + 6 y + 9$

Step 5

Add $5$ and $9$ .

$\frac{5 y}{2} + 6 y + 14$

Step 6

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y}{2} + 6 y \cdot \frac{2}{2} + 14$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Combine $6 y$ and $\frac{2}{2}$ .

$\frac{5 y}{2} + \frac{6 y \cdot 2}{2} + 14$

Step 7.2

Combine the numerators over the common denominator.

$\frac{5 y + 6 y \cdot 2}{2} + 14$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Factor $y$ out of $5 y + 6 y \cdot 2$ .

Tap for more steps...

Step 8.1.1.1

Factor $y$ out of $5 y$ .

$\frac{y \cdot 5 + 6 y \cdot 2}{2} + 14$

Step 8.1.1.2

Factor $y$ out of $6 y \cdot 2$ .

$\frac{y \cdot 5 + y (6 \cdot 2)}{2} + 14$

Step 8.1.1.3

Factor $y$ out of $y \cdot 5 + y (6 \cdot 2)$ .

$\frac{y (5 + 6 \cdot 2)}{2} + 14$

Step 8.1.2

Multiply $6$ by $2$ .

$\frac{y (5 + 12)}{2} + 14$

Step 8.1.3

Add $5$ and $12$ .

$\frac{y \cdot 17}{2} + 14$

Step 8.2

Move $17$ to the left of $y$ .

$\frac{17 y}{2} + 14$