Finite Math Examples

$y = - \frac{1}{2} x + 5$ , $y = 3 x - 2$

Step 1

Eliminate the equal sides of each equation and combine.

$- \frac{1}{2} x + 5 = 3 x - 2$

Step 2

Solve $- \frac{1}{2} x + 5 = 3 x - 2$ for $x$ .

Tap for more steps...

Step 2.1

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

$- \frac{x}{2} + 5 = 3 x - 2$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $3 x$ from both sides of the equation.

$- \frac{x}{2} + 5 - 3 x = - 2$

Step 2.2.2

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} - 3 x \cdot \frac{2}{2} + 5 = - 2$

Step 2.2.3

Combine $- 3 x$ and $\frac{2}{2}$ .

$- \frac{x}{2} + \frac{- 3 x \cdot 2}{2} + 5 = - 2$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{- x - 3 x \cdot 2}{2} + 5 = - 2$

Step 2.2.5

Simplify each term.

Tap for more steps...

Step 2.2.5.1

Simplify the numerator.

Tap for more steps...

Step 2.2.5.1.1

Factor $x$ out of $- x - 3 x \cdot 2$ .

Tap for more steps...

Step 2.2.5.1.1.1

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - 3 x \cdot 2}{2} + 5 = - 2$

Step 2.2.5.1.1.2

Factor $x$ out of $- 3 x \cdot 2$ .

$\frac{x \cdot - 1 + x (- 3 \cdot 2)}{2} + 5 = - 2$

Step 2.2.5.1.1.3

Factor $x$ out of $x \cdot - 1 + x (- 3 \cdot 2)$ .

$\frac{x (- 1 - 3 \cdot 2)}{2} + 5 = - 2$

Step 2.2.5.1.2

Multiply $- 3$ by $2$ .

$\frac{x (- 1 - 6)}{2} + 5 = - 2$

Step 2.2.5.1.3

Subtract $6$ from $- 1$ .

$\frac{x \cdot - 7}{2} + 5 = - 2$

Step 2.2.5.2

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{2} + 5 = - 2$

Step 2.2.5.3

Move the negative in front of the fraction.

$- \frac{7 x}{2} + 5 = - 2$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Subtract $5$ from both sides of the equation.

$- \frac{7 x}{2} = - 2 - 5$

Step 2.3.2

Subtract $5$ from $- 2$ .

$- \frac{7 x}{2} = - 7$

Step 2.4

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 7$

Step 2.5

Simplify both sides of the equation.

Tap for more steps...

Step 2.5.1

Simplify the left side.

Tap for more steps...

Step 2.5.1.1

Simplify $- \frac{2}{7} (- \frac{7 x}{2})$ .

Tap for more steps...

Step 2.5.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.5.1.1.1.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.1.2

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.5.1.1.2.1

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.3

Multiply.

Tap for more steps...

Step 2.5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{7} \cdot - 7$

Step 2.5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{2}{7} \cdot - 7$

Step 2.5.2

Simplify the right side.

Tap for more steps...

Step 2.5.2.1

Simplify $- \frac{2}{7} \cdot - 7$ .

Tap for more steps...

Step 2.5.2.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.5.2.1.1.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$x = \frac{- 2}{7} \cdot - 7$

Step 2.5.2.1.1.2

Factor $7$ out of $- 7$ .

$x = \frac{- 2}{7} \cdot (7 (- 1))$

Step 2.5.2.1.1.3

Cancel the common factor.

$x = \frac{- 2}{7} \cdot (7 \cdot - 1)$

Step 2.5.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 1$

Step 2.5.2.1.2

Multiply $- 2$ by $- 1$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Tap for more steps...

Step 3.1

Substitute $2$ for $x$ .

$y = 3 (2) - 2$

Step 3.2

Simplify $3 (2) - 2$ .

Tap for more steps...

Step 3.2.1

Multiply $3$ by $2$ .

$y = 6 - 2$

Step 3.2.2

Subtract $2$ from $6$ .

$y = 4$

Step 4

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

$(2, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 4)$

Equation Form:

$x = 2, y = 4$

Step 6