Finite Math Examples

$3 x - y = - 15$ , $2 \cdot y = - 19$

Step 1

Divide each term in $2 \cdot y = - 19$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \cdot y = - 19$ by $2$ .

$\frac{2 \cdot y}{2} = \frac{- 19}{2}$

$3 x - y = - 15$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \cdot y}{2} = \frac{- 19}{2}$

$3 x - y = - 15$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 19}{2}$

$3 x - y = - 15$

$y = \frac{- 19}{2}$

$3 x - y = - 15$

$y = \frac{- 19}{2}$

$3 x - y = - 15$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$y = - \frac{19}{2}$

$3 x - y = - 15$

$y = - \frac{19}{2}$

$3 x - y = - 15$

$y = - \frac{19}{2}$

$3 x - y = - 15$

Step 2

Replace all occurrences of $y$ with $- \frac{19}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x - y = - 15$ with $- \frac{19}{2}$ .

$3 x - (- \frac{19}{2}) = - 15$

$y = - \frac{19}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $- (- \frac{19}{2})$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 1$ .

$3 x + 1 (\frac{19}{2}) = - 15$

$y = - \frac{19}{2}$

Step 2.2.1.2

Multiply $\frac{19}{2}$ by $1$ .

$3 x + \frac{19}{2} = - 15$

$y = - \frac{19}{2}$

$3 x + \frac{19}{2} = - 15$

$y = - \frac{19}{2}$

$3 x + \frac{19}{2} = - 15$

$y = - \frac{19}{2}$

$3 x + \frac{19}{2} = - 15$

$y = - \frac{19}{2}$

Step 3

Solve for $x$ in $3 x + \frac{19}{2} = - 15$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{19}{2}$ from both sides of the equation.

$3 x = - 15 - \frac{19}{2}$

$y = - \frac{19}{2}$

Step 3.1.2

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 x = - 15 \cdot \frac{2}{2} - \frac{19}{2}$

$y = - \frac{19}{2}$

Step 3.1.3

Combine $- 15$ and $\frac{2}{2}$ .

$3 x = \frac{- 15 \cdot 2}{2} - \frac{19}{2}$

$y = - \frac{19}{2}$

Step 3.1.4

Combine the numerators over the common denominator.

$3 x = \frac{- 15 \cdot 2 - 19}{2}$

$y = - \frac{19}{2}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $- 15$ by $2$ .

$3 x = \frac{- 30 - 19}{2}$

$y = - \frac{19}{2}$

Step 3.1.5.2

Subtract $19$ from $- 30$ .

$3 x = \frac{- 49}{2}$

$y = - \frac{19}{2}$

$3 x = \frac{- 49}{2}$

$y = - \frac{19}{2}$

Step 3.1.6

Move the negative in front of the fraction.

$3 x = - \frac{49}{2}$

$y = - \frac{19}{2}$

$3 x = - \frac{49}{2}$

$y = - \frac{19}{2}$

Step 3.2

Divide each term in $3 x = - \frac{49}{2}$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = - \frac{49}{2}$ by $3$ .

$\frac{3 x}{3} = \frac{- \frac{49}{2}}{3}$

$y = - \frac{19}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \frac{49}{2}}{3}$

$y = - \frac{19}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{49}{2}}{3}$

$y = - \frac{19}{2}$

$x = \frac{- \frac{49}{2}}{3}$

$y = - \frac{19}{2}$

$x = \frac{- \frac{49}{2}}{3}$

$y = - \frac{19}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{49}{2} \cdot \frac{1}{3}$

$y = - \frac{19}{2}$

Step 3.2.3.2

Multiply $- \frac{49}{2} \cdot \frac{1}{3}$ .

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Step 3.2.3.2.1

Multiply $\frac{1}{3}$ by $\frac{49}{2}$ .

$x = - \frac{49}{3 \cdot 2}$

$y = - \frac{19}{2}$

Step 3.2.3.2.2

Multiply $3$ by $2$ .

$x = - \frac{49}{6}$

$y = - \frac{19}{2}$

$x = - \frac{49}{6}$

$y = - \frac{19}{2}$

$x = - \frac{49}{6}$

$y = - \frac{19}{2}$

$x = - \frac{49}{6}$

$y = - \frac{19}{2}$

$x = - \frac{49}{6}$

$y = - \frac{19}{2}$

Step 4

Solve the system of equations.

$x = - \frac{49}{6} y = - \frac{19}{2}$

Step 5

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

$(- \frac{49}{6}, - \frac{19}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{49}{6}, - \frac{19}{2})$

Equation Form:

$x = - \frac{49}{6}, y = - \frac{19}{2}$

Step 7