Finite Math Examples

$4 x - 3 y = 3$ , $- x - 3 y = 3$

Step 1

Solve for $x$ in $4 x - 3 y = 3$ .

Tap for more steps...

Step 1.1

Add $3 y$ to both sides of the equation.

$4 x = 3 + 3 y$

$- x - 3 y = 3$

Step 1.2

Divide each term in $4 x = 3 + 3 y$ by $4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $4 x = 3 + 3 y$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- x - 3 y = 3$

Step 2

Replace all occurrences of $x$ with $\frac{3}{4} + \frac{3 y}{4}$ in each equation.

Tap for more steps...

Step 2.1

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

$- (\frac{3}{4} + \frac{3 y}{4}) - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$- \frac{3}{4} - \frac{3 y}{4} - 3 y = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.2

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3}{4} - \frac{3 y}{4} - 3 y \cdot \frac{4}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.3

Combine $- 3 y$ and $\frac{4}{4}$ .

$- \frac{3}{4} - \frac{3 y}{4} + \frac{- 3 y \cdot 4}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$- \frac{3}{4} + \frac{- 3 y - 3 y \cdot 4}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{- 3 - 3 y - 3 y \cdot 4}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.6

Multiply $4$ by $- 3$ .

$\frac{- 3 - 3 y - 12 y}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.7

Subtract $12 y$ from $- 3 y$ .

$\frac{- 3 - 15 y}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.8

Factor $3$ out of $- 3 - 15 y$ .

Tap for more steps...

Step 2.2.1.8.1

Factor $3$ out of $- 3$ .

$\frac{3 (- 1) - 15 y}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.8.2

Factor $3$ out of $- 15 y$ .

$\frac{3 (- 1) + 3 (- 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.8.3

Factor $3$ out of $3 (- 1) + 3 (- 5 y)$ .

$\frac{3 (- 1 - 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$\frac{3 (- 1 - 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.9

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{3 (- 1 \cdot 1 - 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.10

Factor $- 1$ out of $- 5 y$ .

$\frac{3 (- 1 \cdot 1 - (5 y))}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.11

Factor $- 1$ out of $- 1 (1) - (5 y)$ .

$\frac{3 (- 1 (1 + 5 y))}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 2.2.1.12

Move the negative in front of the fraction.

$- \frac{3 (1 + 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- \frac{3 (1 + 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- \frac{3 (1 + 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$- \frac{3 (1 + 5 y)}{4} = 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3

Solve for $y$ in $- \frac{3 (1 + 5 y)}{4} = 3$ .

Tap for more steps...

Step 3.1

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} \cdot (- \frac{3 (1 + 5 y)}{4}) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2

Simplify both sides of the equation.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify $- \frac{4}{3} (- \frac{3 (1 + 5 y)}{4})$ .

Tap for more steps...

Step 3.2.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.1.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} \cdot (- \frac{3 (1 + 5 y)}{4}) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.1.2

Move the leading negative in $- \frac{3 (1 + 5 y)}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 (1 + 5 y)}{4} = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 (1 + 5 y)}{4} = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 (1 + 5 y)}{4} = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} \cdot (- 3 (1 + 5 y)) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$\frac{- 1}{3} \cdot (- 3 (1 + 5 y)) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1.2.1

Factor $3$ out of $- 3 (1 + 5 y)$ .

$\frac{- 1}{3} \cdot (3 (- (1 + 5 y))) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 (- (1 + 5 y))) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.2.3

Rewrite the expression.

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.3

Multiply.

Tap for more steps...

Step 3.2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (1 + 5 y) = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.1.1.3.2

Multiply $1 + 5 y$ by $1$ .

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - \frac{4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$1 + 5 y = \frac{- 4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.2.1.2

Cancel the common factor.

$1 + 5 y = \frac{- 4}{3} \cdot 3$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.2.2.1.3

Rewrite the expression.

$1 + 5 y = - 4$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - 4$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - 4$

$x = \frac{3}{4} + \frac{3 y}{4}$

$1 + 5 y = - 4$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Subtract $1$ from both sides of the equation.

$5 y = - 4 - 1$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.3.2

Subtract $1$ from $- 4$ .

$5 y = - 5$

$x = \frac{3}{4} + \frac{3 y}{4}$

$5 y = - 5$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.4

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

Tap for more steps...

Step 3.4.1

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

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

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

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

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

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

$x = \frac{3}{4} + \frac{3 y}{4}$

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

$x = \frac{3}{4} + \frac{3 y}{4}$

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

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Divide $- 5$ by $5$ .

$y = - 1$

$x = \frac{3}{4} + \frac{3 y}{4}$

$y = - 1$

$x = \frac{3}{4} + \frac{3 y}{4}$

$y = - 1$

$x = \frac{3}{4} + \frac{3 y}{4}$

$y = - 1$

$x = \frac{3}{4} + \frac{3 y}{4}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = \frac{3}{4} + \frac{3 y}{4}$ with $- 1$ .

$x = \frac{3}{4} + \frac{3 (- 1)}{4}$

$y = - 1$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{3}{4} + \frac{3 (- 1)}{4}$ .

Tap for more steps...

Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{3 + 3 (- 1)}{4}$

$y = - 1$

Step 4.2.1.2

Simplify the expression.

Tap for more steps...

Step 4.2.1.2.1

Multiply $3$ by $- 1$ .

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

$y = - 1$

Step 4.2.1.2.2

Subtract $3$ from $3$ .

$x = \frac{0}{4}$

$y = - 1$

Step 4.2.1.2.3

Divide $0$ by $4$ .

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 1)$

Equation Form:

$x = 0, y = - 1$

Step 7