Finite Math Examples

$y = 2 x - 7$ , $y = - \frac{1}{2} - 7$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x - 7 = \frac{- 15}{2}$

Step 2

Solve $2 x - 7 = \frac{- 15}{2}$ for $x$ .

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Step 2.1

Move the negative in front of the fraction.

$2 x - 7 = - \frac{15}{2}$

Step 2.2

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

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Step 2.2.1

Add $7$ to both sides of the equation.

$2 x = - \frac{15}{2} + 7$

Step 2.2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 x = - \frac{15}{2} + 7 \cdot \frac{2}{2}$

Step 2.2.3

Combine $7$ and $\frac{2}{2}$ .

$2 x = - \frac{15}{2} + \frac{7 \cdot 2}{2}$

Step 2.2.4

Combine the numerators over the common denominator.

$2 x = \frac{- 15 + 7 \cdot 2}{2}$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $7$ by $2$ .

$2 x = \frac{- 15 + 14}{2}$

Step 2.2.5.2

Add $- 15$ and $14$ .

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

Step 2.2.6

Move the negative in front of the fraction.

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

Step 2.3

Divide each term in $2 x = - \frac{1}{2}$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 x = - \frac{1}{2}$ by $2$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.2

Multiply $- \frac{1}{2} \cdot \frac{1}{2}$ .

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Step 2.3.3.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Step 2.3.3.2.2

Multiply $2$ by $2$ .

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

Step 3

Evaluate $y$ when $x = - \frac{1}{4}$ .

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Step 3.1

Substitute $- \frac{1}{4}$ for $x$ .

$y = \frac{- 15}{2}$

Step 3.2

Move the negative in front of the fraction.

$y = - \frac{15}{2}$

Step 4

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

$(- \frac{1}{4}, - \frac{15}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{4}, - \frac{15}{2})$

Equation Form:

$x = - \frac{1}{4}, y = - \frac{15}{2}$

Step 6