Finite Math Examples

$5 y + 4 x = 0$ , $4 x + 3 y = - \frac{6}{5}$

Step 1

Solve for $y$ in $5 y + 4 x = 0$ .

Tap for more steps...

Step 1.1

Subtract $4 x$ from both sides of the equation.

$5 y = - 4 x$

$4 x + 3 y = - \frac{6}{5}$

Step 1.2

Divide each term in $5 y = - 4 x$ by $5$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $5 y = - 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

$y = \frac{- 4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

$y = \frac{- 4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Move the negative in front of the fraction.

$y = - \frac{4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$4 x + 3 y = - \frac{6}{5}$

Step 2

Replace all occurrences of $y$ with $- \frac{4 x}{5}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $4 x + 3 y = - \frac{6}{5}$ with $- \frac{4 x}{5}$ .

$4 x + 3 (- \frac{4 x}{5}) = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $4 x + 3 (- \frac{4 x}{5})$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Multiply $3 (- \frac{4 x}{5})$ .

Tap for more steps...

Step 2.2.1.1.1.1

Multiply $- 1$ by $3$ .

$4 x - 3 \frac{4 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.1.1.2

Combine $- 3$ and $\frac{4 x}{5}$ .

$4 x + \frac{- 3 (4 x)}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.1.1.3

Multiply $4$ by $- 3$ .

$4 x + \frac{- 12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$4 x + \frac{- 12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.1.2

Move the negative in front of the fraction.

$4 x - \frac{12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$4 x - \frac{12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 x \cdot \frac{5}{5} - \frac{12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.3

Simplify terms.

Tap for more steps...

Step 2.2.1.3.1

Combine $4 x$ and $\frac{5}{5}$ .

$\frac{4 x \cdot 5}{5} - \frac{12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{4 x \cdot 5 - 12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$\frac{4 x \cdot 5 - 12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.4

Simplify the numerator.

Tap for more steps...

Step 2.2.1.4.1

Factor $4 x$ out of $4 x \cdot 5 - 12 x$ .

Tap for more steps...

Step 2.2.1.4.1.1

Factor $4 x$ out of $4 x \cdot 5$ .

$\frac{4 x (5) - 12 x}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.4.1.2

Factor $4 x$ out of $- 12 x$ .

$\frac{4 x (5) + 4 x (- 3)}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.4.1.3

Factor $4 x$ out of $4 x (5) + 4 x (- 3)$ .

$\frac{4 x (5 - 3)}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

$\frac{4 x (5 - 3)}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.4.2

Subtract $3$ from $5$ .

$\frac{4 x \cdot 2}{5} = - \frac{6}{5}$

$y = - \frac{4 x}{5}$

Step 2.2.1.4.3

Multiply $2$ by $4$ .