Finite Math Examples

$y = - \frac{1}{2} x - 1$ , $y = \frac{1}{4} x - 4$

Step 1

Eliminate the equal sides of each equation and combine.

$- \frac{1}{2} x - 1 = \frac{1}{4} x - 4$

Step 2

Solve $- \frac{1}{2} x - 1 = \frac{1}{4} x - 4$ for $x$ .

Tap for more steps...

Step 2.1

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} - 1 = \frac{1}{4} x - 4$

Step 2.2

Combine $\frac{1}{4}$ and $x$ .

$- \frac{x}{2} - 1 = \frac{x}{4} - 4$

Step 2.3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.3.1

Subtract $\frac{x}{4}$ from both sides of the equation.

$- \frac{x}{2} - 1 - \frac{x}{4} = - 4$

Step 2.3.2

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

$- \frac{x}{2} \cdot \frac{2}{2} - \frac{x}{4} - 1 = - 4$

Step 2.3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.3.1

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

$- \frac{x \cdot 2}{2 \cdot 2} - \frac{x}{4} - 1 = - 4$

Step 2.3.3.2

Multiply $2$ by $2$ .

$- \frac{x \cdot 2}{4} - \frac{x}{4} - 1 = - 4$

Step 2.3.4

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 - x}{4} - 1 = - 4$

Step 2.3.5

Simplify each term.

Tap for more steps...

Step 2.3.5.1

Simplify the numerator.

Tap for more steps...

Step 2.3.5.1.1

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

Tap for more steps...

Step 2.3.5.1.1.1

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

$\frac{x (- 1 \cdot 2) - x}{4} - 1 = - 4$

Step 2.3.5.1.1.2

Factor $x$ out of $- x$ .

$\frac{x (- 1 \cdot 2) + x \cdot - 1}{4} - 1 = - 4$

Step 2.3.5.1.1.3

Factor $x$ out of $x (- 1 \cdot 2) + x \cdot - 1$ .

$\frac{x (- 1 \cdot 2 - 1)}{4} - 1 = - 4$

Step 2.3.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (- 2 - 1)}{4} - 1 = - 4$

Step 2.3.5.1.3

Subtract $1$ from $- 2$ .

$\frac{x \cdot - 3}{4} - 1 = - 4$

Step 2.3.5.2

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{4} - 1 = - 4$

Step 2.3.5.3

Move the negative in front of the fraction.

$- \frac{3 x}{4} - 1 = - 4$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Add $1$ to both sides of the equation.

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

Step 2.4.2

Add $- 4$ and $1$ .

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

Step 2.5

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

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

Step 2.6

Simplify both sides of the equation.

Tap for more steps...

Step 2.6.1

Simplify the left side.

Tap for more steps...

Step 2.6.1.1

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

Tap for more steps...

Step 2.6.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.6.1.1.1.1

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

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

Step 2.6.1.1.1.2

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

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

Step 2.6.1.1.1.3

Factor $4$ out of $- 4$ .

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

Step 2.6.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 3$

Step 2.6.1.1.1.5

Rewrite the expression.

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

Step 2.6.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.6.1.1.2.1

Factor $3$ out of $- 3 x$ .

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

Step 2.6.1.1.2.2

Cancel the common factor.

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

Step 2.6.1.1.2.3

Rewrite the expression.

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

Step 2.6.1.1.3

Multiply.

Tap for more steps...

Step 2.6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} \cdot - 3$

Step 2.6.1.1.3.2

Multiply $x$ by $1$ .

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

Step 2.6.2

Simplify the right side.

Tap for more steps...

Step 2.6.2.1

Simplify $- \frac{4}{3} \cdot - 3$ .

Tap for more steps...

Step 2.6.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.6.2.1.1.1

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

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

Step 2.6.2.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.6.2.1.1.3

Cancel the common factor.

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

Step 2.6.2.1.1.4

Rewrite the expression.

$x = - 4 \cdot - 1$

Step 2.6.2.1.2

Multiply $- 4$ by $- 1$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Tap for more steps...

Step 3.1

Substitute $4$ for $x$ .

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

Step 3.2

Substitute $4$ for $x$ in $y = \frac{1}{4} \cdot (4) - 4$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Multiply $\frac{1}{4}$ by $4$ .

$y = \frac{1}{4} \cdot 4 - 4$

Step 3.2.2

Simplify $\frac{1}{4} \cdot 4 - 4$ .

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$y = \frac{1}{4} \cdot 4 - 4$

Step 3.2.2.1.2

Rewrite the expression.

$y = 1 - 4$

Step 3.2.2.2

Subtract $4$ from $1$ .

$y = - 3$

Step 4

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

$(4, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 3)$

Equation Form:

$x = 4, y = - 3$

Step 6