Finite Math Examples

$\frac{x}{2} - \frac{y}{2} = - 1$ , $x + 3 y = - 10$

Step 1

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

$x = - 10 - 3 y$

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

Step 2

Replace all occurrences of $x$ with $- 10 - 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $\frac{x}{2} - \frac{y}{2} = - 1$ with $- 10 - 3 y$ .

$\frac{- 10 - 3 y}{2} - \frac{y}{2} = - 1$

$x = - 10 - 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{- 10 - 3 y}{2} - \frac{y}{2}$ .

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Step 2.2.1.1

Combine the numerators over the common denominator.

$\frac{- 10 - 3 y - y}{2} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.2

Subtract $y$ from $- 3 y$ .

$\frac{- 10 - 4 y}{2} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3

Cancel the common factor of $- 10 - 4 y$ and $2$ .

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Step 2.2.1.3.1

Factor $2$ out of $- 10$ .

$\frac{2 \cdot - 5 - 4 y}{2} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3.2

Factor $2$ out of $- 4 y$ .

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

$x = - 10 - 3 y$

Step 2.2.1.3.3

Factor $2$ out of $2 (- 5) + 2 (- 2 y)$ .

$\frac{2 (- 5 - 2 y)}{2} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3.4

Cancel the common factors.

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Step 2.2.1.3.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 5 - 2 y)}{2 (1)} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3.4.2

Cancel the common factor.

$\frac{2 (- 5 - 2 y)}{2 \cdot 1} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3.4.3

Rewrite the expression.

$\frac{- 5 - 2 y}{1} = - 1$

$x = - 10 - 3 y$

Step 2.2.1.3.4.4

Divide $- 5 - 2 y$ by $1$ .

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

$- 5 - 2 y = - 1$

$x = - 10 - 3 y$

Step 3

Solve for $y$ in $- 5 - 2 y = - 1$ .

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Step 3.1

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

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Step 3.1.1

Add $5$ to both sides of the equation.

$- 2 y = - 1 + 5$

$x = - 10 - 3 y$

Step 3.1.2

Add $- 1$ and $5$ .

$- 2 y = 4$

$x = - 10 - 3 y$

$- 2 y = 4$

$x = - 10 - 3 y$

Step 3.2

Divide each term in $- 2 y = 4$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 y = 4$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - 10 - 3 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - 10 - 3 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{- 2}$

$x = - 10 - 3 y$

$y = \frac{4}{- 2}$

$x = - 10 - 3 y$

$y = \frac{4}{- 2}$

$x = - 10 - 3 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $4$ by $- 2$ .

$y = - 2$

$x = - 10 - 3 y$

$y = - 2$

$x = - 10 - 3 y$

$y = - 2$

$x = - 10 - 3 y$

$y = - 2$

$x = - 10 - 3 y$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 10 - 3 y$ with $- 2$ .

$x = - 10 - 3 \cdot - 2$

$y = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 10 - 3 \cdot - 2$ .

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Step 4.2.1.1

Multiply $- 3$ by $- 2$ .

$x = - 10 + 6$

$y = - 2$

Step 4.2.1.2

Add $- 10$ and $6$ .

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

Step 5

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

$(- 4, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, - 2)$

Equation Form:

$x = - 4, y = - 2$

Step 7